Joint Filing Agreement

                                                                    Exhibit 99.1

                             Joint Filing Agreement

         In accordance with Rule 13d-1(k)(1) promulgated under the Securities
Exchange Act of 1934, as amended, the undersigned agree to the joint filing of a
Statement on Schedule 13D (including any and all amendments thereto) with
respect to the Common Shares, par value $0.01, of Prime Group Realty Trust, and
further agree to the filing of this Agreement as an exhibit thereto. In
addition, each party to this Agreement expressly authorizes each other party to
this Agreement to file on its behalf any and all amendments to such Statement on
Schedule 13D.

Dated: November 2, 2001


                                    VORNADO REALTY TRUST

                                    By: /s/ Xxxxxx Xxxxxx
                                       ----------------------------
                                       Name:  Xxxxxx Xxxxxx
                                       Title: Executive Vice
                                              President-Finance and
                                              Administration, Chief
                                              Financial Officer


                                    VORNADO REALTY L.P.

                                    By: VORNADO REALTY TRUST,
                                        its general partner

                                    By: /s/ Xxxxxx Xxxxxx
                                       ----------------------------
                                       Name:  Xxxxxx Xxxxxx
                                       Title: Executive Vice
                                              President-Finance and
                                              Administration, Chief
                                              Financial Officer


                                    VORNADO PS, L.L.C.

                                    By: VORNADO REALTY L.P.,
                                        its sole member

                                    By: VORNADO REALTY TRUST,
                                        its general partner

                                    By: /s/ Xxxxxx Xxxxxx
                                       ----------------------------
                                       Name:  Xxxxxx Xxxxxx
                                       Title: Executive Vice
                                              President-Finance and
                                              Administration, Chief
                                              Financial Officer