Exhibit 32.1

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

     In connection with the Quarterly Report of Abraxas Petroleum Corporation
(the "Company") on Form 10-Q for the period ending September 30, 2004 as filed
with the Securities and Exchange Commission on the date hereof (the "Report"),
I, Robert L.G. Watson, Chairman of the Board, President and Chief Executive
Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

         (1)  The Report fully complies with the requirements of Section 13(a)
              or 15(d) of the Securities Act of 1934; and

         (2)  The information contained in the Report fairly presents, in all
              material respects, the financial condition and results of
              operations of the Company.

                             /s/ Robert L.G. Watson
                             Robert L.G. Watson
                             Chairman of the Board, President and
                             Chief Executive Officer
                             November 12, 2004




This certification accompanies the Report pursuant to ss.906 of the
Sarbanes-Oxley Act of 2002 and shall not, except to the extent required by the
Sarbanes-Oxley Act of 2002, be deemed filed by the Company for purposes of ss.18
of the Securities Exchange Act of 1964, as amended.

A signed original of this written statement required by Section 906 has been
provided to the Company and will be retained by the Company and furnished to the
Securities and Exchange Commission or its staff upon request.