EXHBIT 4.68 SECOND AMENDMENT TO SECURITY AGREEMENT THIS SECOND AMENDMENT to that certain Security Agreement, dated December 22, 1998, as amended pursuant to that certain Amendment to Security Agreement, dated March 11, 1999 (the "Security Agreement"),...

                                                                     EXHBIT 4.68

                    SECOND AMENDMENT TO SECURITY AGREEMENT


     THIS SECOND AMENDMENT to that certain Security Agreement, dated December
22, 1998, as amended pursuant to that certain Amendment to Security Agreement,
dated March 11, 1999 (the "Security Agreement"), between Tipperary Corporation,
a Texas corporation ("Debtor"), and Slough Estates USA Inc., a Delaware
corporation ("Secured Party"), is made this 19th day of December 2000, between
Debtor and Secured Party.

     WHEREAS, the parties entered into the Security Agreement to secure
performance and payment of certain Promissory Notes, (i) the first, dated
December 22, 1998, payable to Secured Party by Debtor in the amount of
$5,500,000 (the "$5.5 Million Note") and (ii) the second, dated December 22,
1998, payable to Secured Party by Tipperary Oil & Gas (Australia) Pty Ltd. in
the amount of $6,000,000 (the "6.0 Million Note"); and

     WHEREAS, the $5.5 Million Note was surrendered in connection with
additional funds in the amount of $1.0 million loaned by Secured Party to
Debtor, and was replaced by a Promissory Note, dated March 11, 1999 (the "$6.5
Million Note"); and

     WHEREAS, Debtor is executing a Promissory Note, of even date herewith, in
the principal amount of $7.5 million (the "$7.5 Million Note"), in consideration
of the cancellation of the $6.5 Million Note and receipt of $1.0 million loaned
by Secured Party to Debtor; and

     WHEREAS, the parties desire that the Security Agreement and collateral
provided therein shall secure repayment of the $7.5 Million Note in the same
respects as the $6.5 Million Note;

     NOW THEREFORE, in consideration of the loan evidenced by the $7.5 Million
Note and the promises of the parties evidenced thereby and hereby:

     1.   The Security Agreement is hereby amended in that, as of, and after the
execution of the $7.5 Million Note, all references in the Security Agreement to
the "Promissory Notes" shall be deemed to be to the $7.5 Million Note (in place
of the $6.5 Million Note as therein provided before this Second Amendment) and
the $6.0 Million Note.  All provisions in the Security Agreement shall otherwise
remain unchanged, and the Security Agreement shall remain in full force and
effect.


TIPPERARY CORPORATION                   SLOUGH ESTATES USA INC.



By:  /s/ Xxxxx X. Xxxxxxxx              By:  /s/ Xxxxxxx X. Xxxxxx
   -------------------------------         -------------------------------
     Xxxxx X. Xxxxxxxx, President and        Xxxxxxx X. Xxxxxx, Vice President
     Chief Executive Officer                 and Chief Financial Officer