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 Annual  Report of Abraxas  Petroleum  Corporation  (the
"Company")  on Form 10-K for the year ended  December 31, 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
                    March 29, 2005





This  certification  accompanies  the  Report  pursuant  to  Section  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.