COGENT COMMUNICATIONS GROUP, INC. SECOND AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT

COGENT COMMUNICATIONS GROUP, INC. SECOND AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT

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Exhibit 4.2

COGENT COMMUNICATIONS GROUP, INC.

SECOND AMENDED AND RESTATED
REGISTRATION RIGHTS AGREEMENT

March 6, 2003

To ▇▇▇▇ ▇▇▇▇▇▇▇▇▇ (the "Founder") and each of the several holders of Series A Preferred Stock (the "Series A Purchasers"), Series B Preferred Stock (the "Series B Purchasers") Series C Preferred Stock (the "Series C Purchasers"), Series D Preferred Stock (the "Series D Purchasers"), and Series E Preferred Stock (the "Series E Purchasers" and together with the Series D Purchasers, the "Noteholder Purchasers") that are parties hereto (collectively, the "Purchasers"):

Dear Sirs:

This will confirm that in consideration of the Noteholder Purchasers agreement to acquire on the date hereof, subject to the terms and conditions set forth therein, 3,426,293 shares of Series D Preferred Stock and 3,426,293 shares of Series E Preferred Stock of Cogent Communications Group, Inc. (the "Company") pursuant to the Exchange Agreement Dated March , 2003, by and among the Noteholder Purchasers, the Company and Allied Riser Communications Corporation (the "Exchange Agreement") and as an inducement to the Noteholder Purchasers to enter into the Exchange Agreement, the Company covenants and agrees with each of you as follows:

1. Certain Definitions. As used in this Agreement, the following terms shall have the following respective meanings:

"Commission" shall mean the Securities and Exchange Commission, or any other federal agency at the time administering the Securities Act.

"Common Stock" shall mean the Common Stock, par value $.001 per share, of the Company, as constituted as of the date of this Agreement.

"Conversion Shares" shall mean shares of Common Stock issued or issuable upon conversion of the Preferred Stock, and any shares of capital stock received in respect thereof.

"Exchange Act" shall mean the Securities Exchange Act of 1934 or any similar federal statute, and the rules and regulations of the Commission thereunder, all as the same shall be in effect at the time.

"Founder's Common" shall mean the 1,360,000 shares (appropriately adjusted for any subdivision or combination) of Common Stock issued to the Founder (▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇).

"Preferred Stock" shall mean the Series A Preferred Stock, the Series B Preferred Stock, the Series C Preferred Stock, the Series D Preferred Stock, and the Series E Preferred Stock.

"Registration Expenses" shall mean the expenses so described in Section 8.

"Restricted Stock" shall mean (i) the Conversion Shares, excluding Conversion Shares which have been (a) registered under the Securities Act pursuant to an effective registration statement filed thereunder and disposed of in accordance with the registration statement covering them or (b) publicly sold pursuant to Rule 144 under the Securities Act, (ii) the Founder's Common, and (iii) any shares of Common Stock issued or distributed in respect of the securities described in clauses (i) and (ii).

"Securities Act" shall mean the Securities Act of 1933 or any similar federal statute, and the rules and regulations of the Commission thereunder, all as the same shall be in effect at the time.

"Selling Expenses" shall mean the expenses so described in Section 8.

"Series A Preferred Stock" shall mean the Series A Participating Convertible Preferred Stock, par value $.001 per share, of the Company, as constituted as of the date of this Agreement.

"Series B Preferred Stock" shall mean the Series B Participating Convertible Preferred Stock, par value $.001 per share, of the Company, as constituted as of the date of this Agreement.

"Series C Preferred Stock" shall mean the Series C Participating Convertible Preferred Stock, par value $.001 per share, of the Company, as constituted as of the date of this Agreement.

"Series D Preferred Stock" shall mean the Series D Participating Convertible Preferred Stock, par value $.001 per share, of the Company, as constituted as of the date of this Agreement.

"Series E Preferred Stock" shall mean the Series E Participating Convertible Preferred Stock, par value $.001 per share, of the Company, as constituted as of the date of this Agreement.

2. Restrictive Legend. Each certificate representing Preferred Stock, Conversion Shares or Restricted Stock shall, except as otherwise provided in this Section 2 or in Section 3, be stamped or otherwise imprinted with a legend substantially in the following form:

"The securities represented by this certificate have not been registered under the Securities Act of 1933 or applicable state securities laws. These securities have been acquired for investment and not with a view to distribution or resale, and may not be sold mortgaged, pledged, hypothecated or otherwise transferred without an effective registration statement for such securities under the Securities Act of 1933 and applicable state securities laws, or the availability of an exemption from the registration provisions of the Securities Act of 1933 and applicable state securities laws."

A certificate shall not bear such legend if in the opinion of counsel reasonably satisfactory to the Company the securities being sold thereby may be publicly sold without registration under the Securities Act.

3. Notice of Proposed Transfer. Prior to any proposed transfer of any Preferred Stock, Conversion Shares or Restricted Stock (other than under the circumstances described in Sections 4, 5 or 6), the holder thereof shall give written notice to the Company of its intention to effect such transfer. Each such notice shall describe the manner of the proposed transfer and, if requested by the Company, shall be accompanied by an opinion of counsel reasonably satisfactory to the Company to the effect that the proposed transfer may be effected without registration under the Securities Act, whereupon the holder of such stock shall be entitled to transfer such stock in accordance with the terms of its notice; provided, however, that no such opinion of counsel shall be required for a transfer to one or more partners of the transferor (in the case of a transferor that is a partnership), to one or more members of the transferor (in the case of a transferor that is a limited liability company) or to an affiliated corporation (in the case of a transferor that is a corporation); provided, further, however, that any transferee other than a partner, member or affiliate of the transferor shall execute and deliver to the Company a representation letter in form reasonably satisfactory to the Company's counsel to the effect that the transferee is acquiring Restricted Stock for its own account, for investment purposes and without any view to distribution thereof. Each certificate for Preferred Stock or Conversion Shares transferred as above provided shall bear the legend set forth in Section 2, except that such certificate shall not bear such legend if (i) such transfer is in accordance with the provisions of Rule 144 (or any other rule permitting public sale without registration under the Securities Act) or (ii) the opinion of counsel referred to above is to the further effect that the transferee and any subsequent transferee (other than an affiliate of the Company) would be entitled to transfer such securities in a public sale without registration under the Securities Act. The restrictions provided for in this Section 3 shall not apply to securities which are not required to bear the legend prescribed by Section 2 in accordance with the provisions of that Section.

4. Required Registration.

(a) Subject to Section 13(f) of this Agreement, at any time after the earlier of (i) October 16, 2003 and (ii) the date that is six (6) months after the first public

offering of securities by the Company, holders of Restricted Stock constituting more than one-third of the total number of shares of Restricted Stock then outstanding or a lesser percent if the anticipated offering price, net of underwriting discounts and commissions would be at least $5,000,000, may request the Company to register under the Securities Act all or any portion of the shares of Restricted Stock held by such requesting holder or holders for sale in the manner specified in such notice. For purposes of this Section 4 and Sections 5, 6, 13(a) and 13(d), the term "Restricted Stock" shall be deemed to include the number of shares of Restricted Stock which would be issuable to a holder of Preferred Stock upon conversion of all shares of Preferred Stock held by such holder at such time; provided, however, that the only securities which the Company shall be required to register pursuant hereto shall be shares of Common Stock; provided, further, however, that, in any underwritten public offering contemplated by this Section 4 or Sections 5 and 6, the holders of Preferred Stock shall be entitled to sell such Preferred Stock to the underwriters for conversion and sale of the shares of Common Stock issued upon conversion thereof and holders of a majority of the Preferred Stock being so registered shall have the right to approve the managing underwriter(s) selected by the Company in connection with such underwritten public offering. In addition, shares of Founder's Common shall not be deemed Restricted Stock for purposes of this Section 4. Notwithstanding anything to the contrary contained herein, the Company shall not be obligated to effect a registration (i) during the 180 day period commencing with the effective date of a registration statement filed by the Company covering the first firm commitment underwritten public offering after the date hereof or (ii) if the Company delivers notice to the holders of the Restricted Stock within thirty (30) days of any registration request of the Company's intent to file a registration statement for an underwritten public offering within ninety (90) days.

(b) Following receipt of any notice under this Section 4, the Company shall immediately notify all holders of Restricted Stock and Preferred Stock from whom notice has not been received and such holders shall then be entitled within 30 days thereafter to request the Company to include in the requested registration all or any portion of their shares of Restricted Stock. The Company shall use its best efforts to register under the Securities Act, for public sale in accordance with the method of disposition described in paragraph (a) above, the number of shares of Restricted Stock specified in such notice (and in all notices received by the Company from other holders within 30 days after the giving of such notice by the Company). The Company shall be obligated to register Restricted Stock pursuant to this Section 4 on three occasions only; provided, however, that such obligation shall be deemed satisfied only when a registration statement covering all shares of Restricted Stock specified in notices received as aforesaid for sale in accordance with the method of disposition specified by the requesting holders shall have become effective and, if such method of disposition is a firm commitment underwritten public offering, all such shares shall have been sold pursuant thereto.

(c) The Company (or at the option of the Company, the holders of Common Stock) shall be entitled to include in any registration statement referred to in this Section 4, for sale in accordance with the method of disposition specified by the

requesting holders, shares of Common Stock to be sold by the Company or such other holders for its own account, except as and to the extent that, in the opinion of the managing underwriter (if such method of disposition shall be an underwritten public offering), such inclusion would adversely affect the marketing of the Restricted Stock to be sold. Subject to Section 4(a) and except for registration statements on Form ▇-▇, ▇-▇ or any successor thereto, the Company will not file with the Commission any other registration statement with respect to its Common Stock, whether for its own account or that of other stockholders, from the date of receipt of a notice from requesting holders pursuant to this Section 4 until the completion of the period of distribution of the registration contemplated thereby.

(d) If, in the opinion of the managing underwriter, the inclusion of all of the Restricted Stock requested to be registered under this Section would adversely affect the marketing of such shares, the Company shall only include the number of shares that, in the reasonable opinion of such underwriter, can be sold without having an adverse effect on the marketing of such shares, to be allocated as follows: first, to the holders of the Series C Preferred Stock, the Series D Preferred Stock and the Series E Preferred Stock (or the shares of Common Stock issued upon conversion thereof) on a pro rata basis based on the total number of shares of Restricted Stock held by such holders and requested to be included in the registration; second, to the holders of the Series A and Series B Preferred Stock (or the shares of Common Stock issued upon conversion thereof) on a pro rata basis based on the total number of shares of Restricted Stock held by such holders and requested to be included in the registration; and third, to any stockholder of the Company (other than such holders) on a pro rata basis based on the total number of shares held by such holder and requested to be included in the registration; provided however that the number of shares of Restricted Stock to be included in such underwriting and registration shall not be reduced unless all other securities of the Company are first excluded from the underwriting and registration.

5. Incidental Registration. Subject to Section 13(f) of this Agreement, if the Company at any time (other than pursuant to Section 4 or Section 6) proposes to register any of its securities under the Securities Act for sale to the public, whether for its own account or for the account of other security holders or both (except with respect to registration statements on Forms ▇-▇, ▇-▇ or another form not available for registering the Restricted Stock for sale to the public), each such time it will give written notice to all holders of outstanding Restricted Stock of its intention so to do. Upon the written request of any such holder, received by the Company within 30 days after the giving of any such notice by the Company, to register any of its Restricted Stock, the Company will use its best efforts to cause the Restricted Stock as to which registration shall have been so requested to be included in the securities to be covered by the registration statement proposed to be filed by the Company, all to the extent requisite to permit the sale or other disposition by the holder (in accordance with its written request) of such Restricted Stock so registered. In the event that any registration pursuant to this Section 5 shall be, in whole or in part, an underwritten public offering of Common Stock, if the managing underwriter determines in good faith that marketing factors require a limitation of the number of shares to be underwritten, the number of shares that may be included in the

underwriting shall be allocated, first, to the Company; second, to the holders of Restricted Stock invoking the rights under this Section 5 on a pro rata basis based on the total number of shares of Restricted Stock held by such holders; and third, to any stockholder of the Company (other than such holders) on a pro rata basis. No such reduction shall reduce the amount of securities of the selling holders included in the registration below thirty percent (30%) of the total amount of securities included in such registration. Furthermore, unless such offering is the Company's first underwritten public offering of its Common Stock after the date hereof, in the event of a reduction in the total amount of shares included in the registration, the number of shares of Series A and Series B Preferred Stock (or the shares of Common Stock issued upon conversion thereof) shall be reduced prior to any reduction in the number of shares of Series C Preferred Stock, the Series D Preferred Stock or the Series E Preferred Stock (or the shares of Common Stock issued upon conversion thereof). In no event will shares of any other selling stockholder be included in such registration that would reduce the number of shares which may be included by holders of Restricted Stock without the written consent of the holders of not less than sixty-six and two-thirds percent (66²/3%) of the Restricted Stock proposed to be sold in the offering. If any such holder disapproves of the terms of any such underwriting, such holder may elect to withdraw therefrom by written notice to the Company and the underwriter, delivered at least ten (10) business days prior to the effective date of the registration statement. Any shares of Restricted Stock excluded or withdrawn from such underwriting shall be excluded and withdrawn from the registration. For any holder which is a partnership or corporation, the partners, retired partners and stockholders of such holder, or the estates and family members of any such partners and retired partners and any trusts for the benefit of any of the foregoing person shall be deemed to be a single holder, and any pro rata reduction with respect to such holder shall be based upon the aggregate amount of shares carrying registration rights owned by all entities and individuals included in such holder, as defined in this sentence. Notwithstanding the foregoing provisions, the Company may withdraw any registration statement referred to in this Section 5 without thereby incurring any liability to the holders of Restricted Stock.

6. Registration on Form S-3. Subject to Section 13(f) of this Agreement, if at any time (i) a holder or holders of Restricted Stock then outstanding request that the Company file a registration statement on Form S-3 or any successor thereto for a public offering of all or any portion of the shares of Restricted Stock held by such requesting holder or holders, and (ii) the Company is a registrant entitled to use Form S-3 or any successor thereto to register such shares, then the Company shall use its best efforts to register under the Securities Act on Form S-3 or any successor thereto for public sale in accordance with the method of disposition specified in such notice, the number of shares of Restricted Stock specified in such notice. Whenever the Company is required by this Section 6 to use its best efforts to effect the registration of Restricted Stock, each of the procedures and requirements of Section 4 (including but not limited to the requirement that the Company notify all holders of Restricted Stock from whom notice has not been received and provide them with the opportunity to participate in the offering) shall apply to such registration; provided, however, that there shall be no limitation on the number of registrations on Form S-3 which may be requested and obtained under this Section 6 and

registrations effected pursuant to this Section 6 shall not be counted as demands for registration or registrations effected pursuant to Sections 4 or 5, respectively.

(b) Notwithstanding anything to the contrary set forth in this Agreement, the Company's obligation under this Agreement to register Restricted Stock under the Securities Act on registration statements ("Registration Statements") may, upon the reasonable determination of the Board of Directors made not more than twice in the aggregate (and not more than once with respect to a Registration Statement on Form S-1 and not more than once with respect to a Registration Statement on Form S-3 and including any delay pursuant to the last sentence of Section 4(a)) during any 12-month period, be suspended in the event and during such period as unforeseen circumstances (including without limitation (i) an underwritten primary offering by the Company (which includes no secondary offering) if the Company is advised in writing by its underwriters that the registration of the Restricted Stock would have a material adverse effect on the Company's offering, or (ii) pending negotiations relating to, or consummation of, a transaction or the occurrence of an event which would require additional disclosure of material information by the Company in Registration Statements or such other filings, as to which the Company has a bona fide business purpose for preserving confidentiality or which renders the Company unable to comply with the Commission's requirements) exist (such unforeseen circumstances being hereinafter referred to as a "Suspension Event") which would make it impractical or unadvisable for the Company to file the Registration Statements or such other filings or to cause such to become effective. Such suspension shall continue only for so long as such event is continuing but in no event for a period longer than (i) one hundred and twenty (120) days, in the case of a Registration Statement on Form S-1 (or any successor thereto) or (ii) ninety (90) days, in the case of a Registration Statement on Form S-3 (or any successor thereto). The Company shall notify the Purchasers of the existence and nature of any Suspension Event.

7. Registration Procedures. If and whenever the Company is required by the provisions of Sections 4, 5 or 6 to use its best efforts to effect the registration of any shares of Restricted Stock under the Securities Act, the Company will, as expeditiously as possible:

(a) prepare and file with the Commission a registration statement (which, in the case of an underwritten public offering pursuant to Section 4, shall be on Form S-1 or other form of general applicability satisfactory to the managing underwriter selected as therein provided) with respect to such securities and use its best efforts to cause such registration statement to become and remain effective for the period of the distribution contemplated thereby (determined as hereinafter provided);

(b) prepare and file with the Commission such amendments and supplements to such registration statement and the prospectus used in connection therewith as may be necessary to keep such registration statement effective for the period specified in paragraph (a) above and comply with the provisions of the Securities Act with respect to the disposition of all Restricted Stock covered by such registration

statement in accordance with the sellers' intended method of disposition set forth in such registration statement for such period;

(c) furnish to each seller of Restricted Stock and to each underwriter such number of copies of the registration statement and each such amendment and supplement thereto (in each case including all exhibits) and the prospectus included therein (including each preliminary prospectus) as such persons reasonably may request in order to facilitate the public sale or other disposition of the Restricted Stock covered by such registration statement;

(d) use its best efforts to register or qualify the Restricted Stock covered by such registration statement under the securities or "blue sky" laws of such jurisdictions as the sellers of Restricted Stock or, in the case of an underwritten public offering, the managing underwriter reasonably shall request; provided, however, that the Company shall not for any such purpose be required to qualify generally to transact business as a foreign corporation in any jurisdiction where it is not so qualified or to consent to general service of process in any such jurisdiction;

(e) use its best efforts to list the Restricted Stock covered by such registration statement with any securities exchange on which the Common Stock of the Company is then listed;

(f) immediately notify each seller of Restricted Stock and each underwriter under such registration statement, at any time when a prospectus relating thereto is required to be delivered under the Securities Act, of the happening of any event of which the Company has knowledge as a result of which the prospectus contained in such registration statement, as then in effect, includes an untrue statement of a material fact or omits to state a material fact required to be stated therein or necessary to make the statements therein not misleading in light of the circumstances then existing, and promptly prepare and furnish to such seller a reasonable number of copies of a prospectus supplemented or amended so that, as thereafter delivered to the purchasers of such Restricted Stock, such prospectus shall not include an untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein not misleading in light of the circumstances then existing;

(g) if the offering is underwritten and at the request of any seller of Restricted Stock, use its best efforts to furnish on the date that Restricted Stock is delivered to the underwriters for sale pursuant to such registration: (i) an opinion dated such date of counsel representing the Company for the purposes of such registration, addressed to the underwriters and to such seller, to such effect as reasonably may be requested by counsel for the underwriters, and (ii) a letter dated such date from the independent public accountants retained by the Company, addressed to the underwriters and to such seller, stating that they are independent public accountants within the meaning of the Securities Act and that, in the opinion of such accountants, the financial statements of the Company included in the registration statement or the prospectus, or any amendment or supplement thereof, comply as to form in all material respects with the

applicable accounting requirements of the Securities Act, and such letter shall additionally cover such other financial matters (including information as to the period ending no more than five business days prior to the date of such letter) with respect to such registration as such underwriters reasonably may request;

(h) make available for inspection by each seller of Restricted Stock, any underwriter participating in any distribution pursuant to such registration statement, and any attorney, accountant or other agent retained by such seller or underwriter, reasonable access to all financial and other records, pertinent corporate documents and properties of the Company, as such parties may reasonably request, and cause the Company's officers, directors and employees to supply all information reasonably requested by any such seller, underwriter, attorney, accountant or agent in connection with such registration statement;

(i) cooperate with the selling holders of Restricted Stock and the managing underwriters, if any, to facilitate the timely preparation and delivery of certificates representing Restricted Stock to be sold, such certificates to be in such denominations and registered in such names as such holders or the managing underwriters may request at least two business days prior to any sale of Restricted Stock; and

(j) permit any holder of Restricted Stock which holder, in the sole and exclusive judgment, exercised in good faith, of such holder, might be deemed to be a controlling person of the Company, to participate in good faith in the preparation of such registration or comparable statement and to require the insertion therein of material, furnished to the Company in writing, which in the reasonable judgment of such holder and its counsel should be included and to permit any other holder of Restricted Stock participating in the registration to review such registration or comparable statement during its preparation.

For purposes of Section 7(a) and 7(b) and of Section 4(c), the period of distribution of Restricted Stock in a firm commitment underwritten public offering shall be deemed to extend until each underwriter has completed the distribution of all securities purchased by it, and the period of distribution of Restricted Stock in any other registration shall be deemed to extend until the earlier of the sale of all Restricted Stock covered thereby and 180 days after the effective date thereof.

In connection with each registration hereunder, the sellers of Restricted Stock will furnish to the Company in writing such information requested by the Company with respect to themselves and the proposed distribution by them as reasonably shall be necessary in order to assure compliance with federal and applicable state securities laws and to make the registration statement correct, accurate and complete in all respects with respect to such sellers; provided, however, that this requirement shall not be deemed to limit any disclosure obligation arising out of any seller's relationship to the Company if one of such seller's agents or affiliates is an officer, director or control person of the Company. In addition, the sellers shall, if requested by the Company, execute such other

agreements, which are reasonably satisfactory to them and which shall contain such provisions as may be customary and reasonable in order to accomplish the registration of the Restricted Stock.

In connection with each registration pursuant to Sections 4, 5 or 6 covering an underwritten public offering, the Company and each seller agree to enter into a written agreement with the managing underwriter selected in the manner herein provided in such form and containing such provisions as are customary in the securities business for such an arrangement between such underwriter and companies of the Company's size and investment stature.

8. Expenses. All expenses incurred by the Company in complying with Sections 4, 5 and 6, including, without limitation, all registration and filing fees, printing expenses, fees and disbursements of counsel and independent public accountants for the Company, fees and expenses (including counsel fees) incurred in connection with complying with state securities or "blue sky" laws, fees and expenses of one counsel for the selling holders of Restricted Stock in connection with the registration of Restricted Stock, fees of the National Association of Securities Dealers, Inc., transfer taxes, fees of transfer agents and registrars, costs of any insurance which might be obtained, but excluding any Selling Expenses, are called "Registration Expenses." All underwriting discounts and selling commissions applicable to the sale of Restricted Stock and the fees and expenses of more than one counsel for the selling holders of Restricted Stock in connection with the registration of Restricted Stock are called "Selling Expenses."

The Company will pay all Registration Expenses in connection with each registration statement under Sections 4, 5 or 6. All Selling Expenses in connection with each registration statement under Sections 4, 5 or 6 shall be borne by the participating sellers in proportion to the number of shares sold by each, or by such participating sellers other than the Company (except to the extent the Company shall be a seller) as they may agree.

9. Indemnification.

(a) To the extent permitted by law, in the event of a registration of any of the Restricted Stock under the Securities Act pursuant to Sections 4, 5 or 6, the Company will indemnify and hold harmless each holder of Restricted Stock, its partners, members, officers and directors, each underwriter of such Restricted Stock thereunder and each other person, if any, who controls such seller or underwriter within the meaning of the Securities Act, against any losses, claims, damages or liabilities, joint or several, to which such holder, officer, director, underwriter or controlling person may become subject under the Securities Act, Exchange Act or otherwise, insofar as such losses, claims, damages or liabilities (or actions in respect thereof) arise out of or are based upon (i) any untrue statement or alleged untrue statement of any material fact contained in any registration statement under which such Restricted Stock was registered under the Securities Act pursuant to Sections 4, 5 or 6, any preliminary prospectus (but only to the extent not corrected in the final prospectus) or final prospectus contained therein, or any

amendment or supplement thereof, (ii) any blue sky application or other document executed by the Company specifically for that purpose or based upon written information furnished by the Company filed in any state or other jurisdiction in order to qualify any or all of the Restricted Stock under the securities laws thereof (any such application, document or information herein called a "Blue Sky Application"), (iii) the omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, (iv) any violation by the Company or its agents of any rule or regulation promulgated under the Securities Act or Exchange Act applicable to the Company or its agents and relating to action or inaction required of the Company in connection with such registration, or (v) any failure to register or qualify the Restricted Stock in any state where the Company or its agents has affirmatively undertaken or agreed in writing that the Company (the undertaking of any underwriter chosen by the Company being attributed to the Company) will undertake such registration or qualification on the seller's behalf (provided that in such instance the Company shall not be so liable if it has undertaken its best efforts to so register or qualify the Restricted Stock) and will reimburse each such holder, and such partner, member, officer and director, each such underwriter and each such controlling person for any legal or other expenses reasonably incurred by them in connection with investigating or defending any such loss, claim, damage, liability or action; provided, however, that the Company will not be liable in any such case if and to the extent that any such loss, claim, damage or liability arises out of or is based upon an untrue statement or alleged untrue statement or omission or alleged omission so made in conformity with information furnished by any such seller, any such underwriter or any such controlling person in writing specifically for use in such registration statement, prospectus or Blue Sky Application.

(b) To the extent permitted by law, in the event of a registration of any of the Restricted Stock under the Securities Act pursuant to Sections 4, 5 or 6, each seller of such Restricted Stock thereunder, severally and not jointly, will indemnify and hold harmless the Company, each person, if any, who controls the Company within the meaning of the Securities Act, each officer of the Company who signs the registration statement, each director of the Company, each other holder of Restricted Stock, each underwriter and each person who controls any underwriter within the meaning of the Securities Act, against all losses, claims, damages or liabilities, joint or several, to which the Company or such officer, director, other seller, underwriter or controlling person may become subject under the Securities Act, Exchange Act or otherwise, insofar as such losses, claims, damages or liabilities (or actions in respect thereof) arise out of or are based upon any untrue statement or alleged untrue statement of any material fact contained in the registration statement under which such Restricted Stock was registered under the Securities Act pursuant to Sections 4, 5 or 6, any preliminary prospectus (but only to the extent not corrected in the final prospectus) or final prospectus contained therein, or any amendment or supplement thereof, or any Blue Sky Application or arise out of or are based upon the omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, and will reimburse the Company and each such officer, director, other seller, underwriter and controlling person for any legal or other expenses reasonably incurred by them in

connection with investigating or defending any such loss, claim, damage, liability or action; provided, however, that such seller will be liable hereunder in any such case if and only to the extent that any such loss, claim, damage or liability arises out of or is based upon an untrue statement or alleged untrue statement or omission or alleged omission made in reliance upon and in conformity with information pertaining to such seller, as such, furnished in writing to the Company by such seller specifically for use in such registration statement, prospectus or Blue Sky Application; and provided, further, however, that the liability of each seller hereunder shall be limited to the proportion of any such loss, claim, damage, liability or expense which is equal to the proportion that the public offering price of the shares sold by such seller under such registration statement bears to the total public offering price of all securities sold thereunder, but not in any event to exceed the net proceeds received by such seller from the sale of Restricted Stock covered by such registration statement.

(c) Promptly after receipt by an indemnified party hereunder of notice of the commencement of any action, such indemnified party shall, if a claim in respect thereof is to be made against the indemnifying party hereunder, notify the indemnifying party in writing thereof, but the omission so to notify the indemnifying party shall not relieve it from any liability which it may have to such indemnified party other than under this Section 9 and shall only relieve it from any liability which it may have to such indemnified party under this Section 9 if and to the extent the indemnifying party is prejudiced by such omission. In case any such action shall be brought against any indemnified party and it shall notify the indemnifying party of the commencement thereof, the indemnifying party shall be entitled to participate in and, to the extent it shall wish, to assume and undertake the defense thereof with counsel satisfactory to such indemnified party, and, after notice from the indemnifying party to such indemnified party of its election so to assume and undertake the defense thereof, the indemnifying party shall not be liable to such indemnified party under this Section 9 for any legal expenses subsequently incurred by such indemnified party in connection with the defense thereof other than reasonable costs of investigation and of liaison with counsel so selected; provided, however, that, if the defendants in any such action include both the indemnified party and the indemnifying party and the indemnified party shall have reasonably concluded that the interests of the indemnified party reasonably may be deemed to conflict with the interests of the indemnifying party, the indemnified party shall have the right to select a separate counsel and to assume such legal defenses and otherwise to participate in the defense of such action, with the expenses and fees of such separate counsel and other expenses related to such participation to be reimbursed by the indemnifying party as incurred. No indemnifying party, in the defense of any such claim or litigation shall, except with the consent of each indemnified party, consent to entry of any judgment or enter into any settlement which does not include as an unconditional term thereof the giving by the claimant or plaintiff to such indemnified party of a release from all liability in respect of such claim or litigation, and no indemnified party shall consent to entry of any judgment or settle such claim or litigation without the prior written consent of the indemnifying party, which consent shall not be unreasonably withheld.

(d) If the indemnification provided for in this Section 9 is held by a court of competent jurisdiction to be unavailable to an indemnified party with respect to any losses, claims, damages or liabilities referred to herein, the indemnifying party, in lieu of indemnifying such indemnified party thereunder, shall to the extent permitted by applicable law contribute to the amount paid or payable by such indemnified party as a result of such loss, claim, damage or liability in such proportion as is appropriate to reflect the relative fault of the indemnifying party on the one hand and of the indemnified party on the other in connection with the violation that resulted in such loss, claim, damage or liability, as well as any other relevant equitable considerations. The relative fault of the indemnifying party and of the indemnified party shall be determined by a court of law by reference to, among other things, whether the untrue or alleged untrue statement of a material fact or the omission or alleged omission to state a material fact relates to information supplied by the indemnifying party or by the indemnified party and the parties' relative intent, knowledge, access to information and opportunity to correct or prevent such statement or omission; provided, however, that in no event shall any contribution by a holder of Restricted Stock hereunder exceed the net proceeds from the offering received by such holder.

(e) The obligations of the Company and holders of Restricted Stock under this Section 9 shall survive completion of any offering of Restricted Stock by a registration statement and the termination of this Agreement.

10. Changes in Common Stock, Series A Preferred Stock, Series B Preferred Stock, Series C Preferred Stock, Series D Preferred Stock or Series E Preferred Stock. If, and as often as, there is any change in the Common Stock, the Series A Preferred Stock, the Series B Preferred Stock, the Series C Preferred Stock, Series D Preferred Stock or Series E Preferred Stock by way of a stock split, stock dividend, combination or reclassification, or through a merger, consolidation, reorganization or recapitalization, or by any other means, appropriate adjustment shall be made in the provisions hereof so that the rights and privileges granted hereby shall continue with respect to the Common Stock, the Series A Preferred Stock, the Series B Preferred Stock, the Series C Preferred Stock, Series D Preferred Stock or Series E Preferred Stock as so changed.

11. Rule 144 Reporting. With a view to making available the benefits of certain rules and regulations of the Commission which may at any time permit the sale of the Restricted Stock to the public without registration, at all times after 90 days after any registration statement covering a public offering of securities of the Company under the Securities Act shall have become effective, the Company agrees to:

(a) make and keep public information available, as those terms are understood and defined in Rule 144 under the Securities Act;

(b) use its best efforts to file with the Commission in a timely manner all reports and other documents required of the Company under the Securities Act and the Exchange Act; and

(c) furnish to each holder of Restricted Stock forthwith upon request a written statement by the Company as to its compliance with the reporting requirements of such Rule 144 and of the Securities Act and the Exchange Act, a copy of the most recent annual or quarterly report of the Company, and such other reports and documents so filed by the Company as such holder may reasonably request in availing itself of any rule or regulation of the Commission allowing such holder to sell any Restricted Stock without registration.

12. Representations and Warranties of the Company. The Company represents and warrants to you as follows:

(a) The execution, delivery and performance of this Agreement by the Company have been duly authorized by all requisite corporate action and will not violate any provision of law, any order of any court or other agency of government, the articles of organization or By-laws of the Company or any provision of any indenture, agreement or other instrument to which it or any or its properties or assets is bound, conflict with, result in a breach of or constitute (with due notice or lapse of time or both) a default under any such indenture, agreement or other instrument or result in the creation or imposition of any lien, charge or encumbrance of any nature whatsoever upon any of the properties or assets of the Company.

(b) This Agreement has been duly executed and delivered by the Company and constitutes the legal, valid and binding obligation of the Company, enforceable in accordance with its terms.

13. Miscellaneous.

(a) All covenants and agreements contained in this Agreement by or on behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors and assigns of the parties hereto (including without limitation transferees of any Preferred Stock or Restricted Stock), whether so expressed or not; provided, however, that registration rights conferred herein on the holders of Preferred Stock or Restricted Stock shall only inure to the benefit of a transferee of Preferred Stock or Restricted Stock if (i) there is transferred to such transferee at least twenty five percent (25%) of the shares of Restricted Stock (appropriately adjusted for any subdivision or combination) originally issued to a Purchaser, (ii) such transferee is a member, former member, partner, retired partner, family member or trust for the benefit of any individual holder, stockholder or affiliate of a party hereto or (iii) such transferee acquires at least 2,500,000 shares (appropriately adjusted for any subdivision or combination) of Preferred Stock; provided, further, however, that the Company is given written notice thereof.

(b) All notices, requests, consents and other communications hereunder shall be in writing and shall be mailed by certified or registered mail, return receipt requested, postage prepaid, or by recognized overnight delivery service of international reputation or, in the case of non-U.S. residents, telexed or sent by recognized overnight delivery service of international reputation or, addressed as follows:

If to the Company, to:

Cogent Communications Group, Inc.
▇▇▇▇ ▇▇▇▇ ▇▇▇▇▇▇, ▇.▇.
▇▇▇▇▇▇▇▇▇▇, ▇▇ ▇▇▇▇▇,
Attention: ▇▇▇▇▇▇ ▇▇▇▇▇

with copies to:

▇▇▇▇▇▇ & ▇▇▇▇▇▇▇
▇▇▇ ▇▇▇▇▇▇▇▇ ▇▇., ▇.▇., ▇▇▇▇▇ ▇▇▇▇
▇▇▇▇▇▇▇▇▇▇, ▇.▇. ▇▇▇▇▇
Attention: ▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇

If or any other party hereto, to their respective addresses set forth on Schedule I hereto;

If to any subsequent holder of Preferred Stock or Restricted Stock, to it at such address as may have been furnished to the Company in writing by such holder;

or, in any case, at such other address or addresses as shall have been furnished in writing to the Company (in the case of a holder of Preferred Stock or Restricted Stock) or to the holders of Preferred Stock or Restricted Stock (in the case of the Company) in accordance with the provisions of this paragraph.

(d) This Agreement may not be amended or modified, and no provision hereof may be waived, without the written consent of the Company and the holders of at least two-thirds of the outstanding shares of Restricted Stock. Notwithstanding the foregoing, no such amendment or modification shall be effective if and to the extent that such amendment or modification either (a) creates any additional affirmative obligations to be complied with by any or all of the Purchasers or (b) grants to any one or more Purchasers any rights more favorable than any rights granted to all other Purchasers or otherwise treats any one or more Purchasers differently than all other Purchasers.

(e) This Agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

(f) If requested in writing by the underwriters for the first underwritten public offering of securities of the Company after the date hereof, each holder of Restricted Stock who is a party to this Agreement shall agree not to sell

publicly any shares of Restricted Stock or any other shares of Common Stock (other than shares of Restricted Stock or other shares of Common Stock being registered in such offering or any shares purchased in the open market after the Company's public offering), without the consent of such underwriters, for a period of not more than 180 days following the consummation of such public offering; provided, however, that all holders of at least one percent (1%) of the then outstanding Common Stock and all officers and directors of the Company shall also have agreed not to sell publicly their Common Stock under the circumstances and pursuant to the terms set forth in this Section 13(f).

(g) If any provision of this Agreement shall be held to be illegal, invalid or unenforceable, such illegality, invalidity or unenforceability shall attach only to such provision and shall not in any manner affect or render illegal, invalid or unenforceable any other provision of this Agreement, and this Agreement shall be carried out as if any such illegal, invalid or unenforceable provision were not contained herein.

(h) Upon and after the Closing (as defined in the Exchange Agreement), this Agreement shall amend and restate in its entirety the Amended Registration Rights Agreement, dated October 16, 2001, by and among the Company, the Founder and the other parties thereto, the parties hereto constitute the Company and the holders of at least two-thirds of the outstanding shares of Restricted Stock immediately prior to the execution of this Agreement.

(i) After the date of this Agreement, the Company shall not, without the prior written consent of the holders of at least two-thirds of the Restricted Stock then outstanding, enter into any agreement with any holder or prospective holder of any securities of the Company that would grant such holder registration rights pari passu or senior to those granted to the holders hereunder, other than (i) with respect to any warrants issued to Cisco Systems Capital Corporation or its affiliates in connection with the Company's increase of its credit facility with Cisco Systems or (ii) a registration related to stock issued upon conversion of debt securities assumed by the Company in connection with its acquisition of Allied Riser Communications Corporation.

(j) All registration rights granted under Sections 4, 5, and 6 shall terminate and be of no further force and effect upon the earlier of (i) three (3) years after the date the Company first effects a registration pursuant to Section 4 or (ii) five (5) years from the date hereof. In addition, the registration rights of a holder of Restricted Stock shall expire if all Restricted Stock held by and issuable to such holder (and its affiliates) may be sold under Rule 144 during any ninety (90) day period.

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Please indicate your acceptance of the foregoing by signing and returning the enclosed counterpart of this letter, whereupon this Agreement shall be a binding agreement between the Company and you.

Very truly yours,
COGENT COMMUNICATIONS GROUP, INC.
By:	/s/ ▇▇▇▇ ▇▇▇▇▇▇▇▇▇
	Name:	▇▇▇▇ ▇▇▇▇▇▇▇▇▇
	Title:	President
PURCHASERS:
OAK INVESTMENT PARTNERS IX, LIMITED PARTNERSHIP
By:	Oak Associates IX, LLC, its General Partner
By:	/s/ ▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇▇▇
	Name:	▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇▇▇
	Title:
OAK IX AFFILIATES FUND, LIMITED PARTNERSHIP
By:	Oak IX Affiliates, LLC, its General Partner
By:	/s/ ▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇▇▇
	Name:	▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇▇▇
	Title:
OAK IX AFFILIATES FUND-A, LIMITED PARTNERSHIP
By:	Oak Associates IX, LLC, its General Partner
By:	/s/ ▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇▇▇
	Name:	▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇▇▇
	Title:

[Signature Page to Registration Rights Agreement—Continued]

JERUSALEM VENTURE PARTNERS III, L.P.
By:	Jerusalem Partners III, L.P., its General Partner
By:	Jerusalem Venture Partners Corporation, its General Partner
By:	/s/ EREL ▇. ▇▇▇▇▇▇▇▇
	Name:	Erel ▇. ▇▇▇▇▇▇▇▇
	Title:
JERUSALEM VENTURE PARTNERS III (ISRAEL), L.P.
By:	Jerusalem Venture Partners III (Israel) Management Company Ltd., its General Partner
By:	/s/ EREL ▇. ▇▇▇▇▇▇▇▇
	Name:	Erel ▇. ▇▇▇▇▇▇▇▇
	Title:
JERUSALEM VENTURE PARTNERS ENTREPRENEURS FUND III, L.P.
By:	Jerusalem Partners III, L.P., its General Partner
By:	/s/ EREL ▇. ▇▇▇▇▇▇▇▇
	Name:	Erel ▇. ▇▇▇▇▇▇▇▇
	Title:

[Signature Page to Registration Rights Agreement—Continued]

JERUSALEM VENTURE PARTNERS IV, L.P.
By:	Jerusalem Partners IV, L.P., its General Partner
By:	Jerusalem Venture Partners Corporation IV, its General Partner
By:	/s/ EREL ▇. ▇▇▇▇▇▇▇▇
	Name:	Erel ▇. ▇▇▇▇▇▇▇▇
	Title:
JERUSALEM VENTURE PARTNERS IV (Israel), L.P.
By:	Jerusalem Partners IV—Venture Capital, L.P., its General Partner
By:	Jerusalem Venture Partners Corporation IV, its General Partner
By:	/s/ EREL ▇. ▇▇▇▇▇▇▇▇
	Name:	Erel ▇. ▇▇▇▇▇▇▇▇
	Title:
JERUSALEM VENTURE PARTNERS IV-A, L.P.
By:	Jerusalem Venture Partners IV, L.P., its General Partner
By:	Jerusalem Venture Partners Corporation IV, its General Partner
By:	/s/ EREL ▇. ▇▇▇▇▇▇▇▇
	Name:	Erel ▇. ▇▇▇▇▇▇▇▇
	Title:

[Signature Page to Registration Rights Agreement—Continued]

		WORLDVIEW TECHNOLOGY PARTNERS III, L.P.
		WORLDVIEW TECHNOLOGY INTERNATIONAL III, L.P.
		WORLDVIEW STRATEGIC PARTNERS III, L.P.
		WORLDVIEW III CARRIER FUND, L.P.
		By:		Worldview Capital III, L.P., its General Partner
		By:		Worldview Equity I, L.L.C., its General Partner
		By:		/s/ ▇▇▇▇▇ ▇▇▇
		Name: ▇▇▇▇▇ ▇▇▇—Member Wei
		WORLDVIEW TECHNOLOGY PARTNERS IV, L.P.
		WORLDVIEW TECHNOLOGY INTERNATIONAL IV, L.P.
		WORLDVIEW STRATEGIC PARTNERS IV, L.P.
		By:		Worldview Capital IV, L.P., its General Partner
		By:		Worldview Equity I, L.L.C., its General Partner
		By:		/s/ ▇▇▇▇▇ ▇▇▇
		Name: ▇▇▇▇▇ ▇▇▇—Member Wei

[Signature Page to Registration Rights Agreement—Continued]

BROADVIEW CAPITAL PARTNERS L.P.
By:	Broadview Capital Partners Management LLC, its General Partner
By:	/s/ ▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇
	Name:	▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇
	Title:	Managing Director
BROADVIEW CAPITAL PARTNERS QUALIFIED PURCHASER FUND L.P.
By:	Broadview Capital Partners Management LLC, its General Partner
By:	/s/ ▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇
	Name:	▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇
	Title:	Managing Director
BROADVIEW CAPITAL PARTNERS AFFILIATES FUND LLC
By:	Broadview Capital LLC, its Manager
By:	/s/ ▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇
	Name:	▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇
	Title:	Managing Director

[Signature Page to Registration Rights Agreement—Continued]

BOULDER VENTURES III, L.P.
By:	/s/ ▇▇▇▇▇▇ ▇. ▇▇▇▇▇
	Name:	▇▇▇▇▇▇ ▇. ▇▇▇▇▇
	Title:	General Partner
BOULDER VENTURES III (ANNEX), L.P.
By:	/s/ ▇▇▇▇▇▇ ▇. ▇▇▇▇▇
	Name:	▇▇▇▇▇▇ ▇. ▇▇▇▇▇
	Title:	General Partner

[Signature Page to Registration Rights Agreement—Continued]

/s/ ▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇

▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇

[Signature Page to Registration Rights Agreement—Continued]

		ANDA PARTNERSHIP By it Partners
				▇▇▇ ONLY TRUST
				/s/ ▇▇▇▇ ▇▇▇▇▇▇ By: ▇▇▇▇ ▇▇▇▇▇▇ Title: Co-Trustee
				▇▇▇ AND DESCENDANTS TRUST
				/s/ ▇▇▇▇ ▇▇▇▇▇▇ By: ▇▇▇▇ ▇▇▇▇▇▇ Title: Co-Trustee

[Signature Page to Registration Rights Agreement—Continued]

[Signature Page to Registration Rights Agreement—Continued]

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[Signature Page to Registration Rights Agreement—Continued]

[Signature Page to Registration Rights Agreement—Continued]

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[Signature Page to Registration Rights Agreement—Continued]

[Signature Page to Registration Rights Agreement—Continued]

[Signature Page to Registration Rights Agreement—Continued]

QuickLinks

Exhibit 4.2

COGENT COMMUNICATIONS GROUP, INC. SECOND AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT

CRT CAPITAL GROUP, LLC

/s/ C. ▇▇▇▇▇▇▇ ▇▇▇▇▇▇

C. ▇▇▇▇▇▇▇ ▇▇▇▇▇▇