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                                                                     EXHIBIT 4.5


                                FIRST AMENDMENT
                                       TO
                       CONTINGENT VALUE RIGHTS AGREEMENT

         This First Amendment to Contingent Value Rights Agreement ("First
Amendment") dated as of May 2, 1996 by and between Abraxas Petroleum
Corporation, a Nevada corporation (the "Company"), and First Union National
Bank of North Carolina (the "Rights Agent").

                              W I T N E S S E T H:

         WHEREAS, the Company and the Rights Agent have previously executed and
delivered that certain Contingent Value Rights Agreement dated as of November
17, 1995 (the "Original Agreement" and, together with this First Amendment, the
"Agreement");

         WHEREAS, the Company's Board of Directors has approved this First
Amendment;

         NOW, THEREFORE, in consideration of the mutual covenants and
agreements herein contained, the Company and the Rights Agent agree as follows:

         1.      Unless otherwise defined in this First Amendment, all
capitalized terms used herein shall have the meaning set forth in the Original
Agreement.

         2.      Section 1.05(b) of the Original Agreement is hereby amended to
read, in its entirety, as follows:

         "(b)    the Company by the Rights Agent or by any Holder shall be
         sufficient for every purpose hereunder if in writing and mailed,
         first-class postage prepaid, to the Company addressed to it at 500
         North Loop 1604 East, Suite 100, San Antonio, Texas 78232 Attention:
         Chief Financial Officer, or at any other address previously furnished
         in writing to the Rights Agent by the Company."

         3.      Section 8.01(c) is hereby added to the Original Agreement and
reads, in its entirety, as follows:

         "(c)    In the event that the Company shall consolidate with or merge
         into any other Person or convey, transfer or lease its properties and
         assets substantially as an entirety to any Person or is liquidated
         (each, a "Transaction"), the Holders of the CVRs shall be entitled to
         receive shares of the capital stock or securities
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         of the Surviving Person or such other consideration that holders of
         shares of the Common Stock received in such a Transaction as follows:

                 (1)      in the event of a Transaction in which the
                          consideration received by the holders of the Common
                          Stock is shares of the capital stock or other
                          securities of the Surviving Person, the Surviving
                          Person shall issue to each Holder of a CVR
                          Certificate at the Maturity Date, unless the
                          Surviving Person shall, in its sole discretion,
                          extend the Maturity Date to the Extended Maturity
                          Date, then at the Extended Maturity Date, for each
                          CVR held by such Holder, upon presentment by such
                          Holder of such Holder's CVR Certificate, the number
                          of shares of capital stock or other securities of the
                          Surviving Person equal to a fraction, the numerator
                          of which is the Adjusted Target Price (as defined
                          below) minus the Adjusted Current Market Value (as
                          defined below) per share and the denominator of which
                          is the Adjusted Current Market Value per share;
                          provided, however, in no event shall the Surviving
                          Person (a) be required to issue a number of shares of
                          its capital stock or other securities greater than
                          (i) 1.0 times the Conversion Ratio (as defined below)
                          on the Maturity Date or (ii) 1.5 times the Conversion
                          Ratio on the Extended Maturity Date and (b) issue
                          shares of its capital stock or other securities which
                          are not publicly traded to the Holders for any CVRs
                          held by them.  In the event that the shares of
                          capital stock or other securities of the Surviving
                          Person to be issued in a Transaction are not publicly
                          traded, the consideration to be received by the
                          Holders for any CVRs held by them in a Transaction
                          shall be cash in accordance with the terms of Section
                          8.01(c)(2) hereof.  All determinations by the
                          Surviving Person in connection with this Section
                          8.01(c), absent manifest error, shall be final and
                          binding on the Surviving Person and the Holders;

                 (2)      in the event of a Transaction in which the holders of
                          Common Stock receive cash, the Surviving Person shall
                          pay to each Holder of a CVR Certificate, on the
                          effective date of such a Transaction, for each CVR
                          held by such Holder, upon presentment by such Holder
                          of such Holder's CVR Certificate, an amount of cash
                          equal to the Target Price minus the amount of cash
                          received by the stockholders of the Company for one
                          share of the Common Stock; provided, however, (i) in
                          no event shall any Holder receive greater than $5.00
                          per CVR on or prior to the Maturity Date and $7.50
                          per CVR from and after the Maturity Date to and
                          including the Extended Maturity Date and (ii) that in
                          the event that the amount of cash per share received
                          by the holders of the Common Stock is greater than
                          the Target Price, the Holders shall not receive any
                          cash for any CVRs held by them.





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                 (3)      As used in this Section 8.01(c), the following
                          capitalized terms shall have the following meanings:

                          (i)     "Adjusted Current Market Value" per share
                          means, with respect to the Maturity Date or the
                          Extended Maturity Date, the median of the averages of
                          the closing bid prices of the shares of capital stock
                          or other securities of the Surviving Person received
                          by the holders of Common Stock in a Transaction on
                          the principal stock exchange on which such shares of
                          capital stock or other securities are traded during
                          each 20 consecutive Trading Day period that both
                          begins and ends in the Valuation Period;

                          (ii)    "Adjusted Target Price" means the Target 
                          Price divided by the Conversion Ratio; and

                          (iii)   "Conversion Ratio" means the number of shares
                          of capital stock or other securities of the Surviving
                          Person received by the Holder of one (1) share of the
                          Common Stock."

         3.      Except as expressly amended hereby, the Original Agreement
remains in full force and effect.  Any references to the Original Agreement in
the CVR Certificates shall refer to the Agreement as amended hereby.





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         IN WITNESS WHEREOF, the parties have executed this Amendment as of the
date first written above.


                                           ABRAXAS PETROLEUM CORPORATION



                                           By:                                 
                                               --------------------------------
                                              Robert L. G. Watson,
                                              Chairman of the Board,
                                              Chief Executive Officer and
                                              President


ATTEST:

                                              
- --------------------------------
Stephen T. Wendel, Secretary



                                           FIRST UNION NATIONAL BANK OF
                                           NORTH CAROLINA



                                           By:                                 
                                               --------------------------------
                                           Title:                              
                                                 ------------------------------





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