EXHIBIT 32.1

                           SECTION 1350 CERTIFICATION

         In connection with the Quarterly Report of Encore Acquisition Company
(the "Company") on Form 10-Q for the period ending September 30, 2003 as filed
with the Securities and Exchange Commission on the date hereof (the "Report"),
I, I. Jon Brumley, 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 Exchange Act of 1934; and

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



         Date: November 7, 2003

                                                /s/ I. Jon Brumley
                                             ----------------------------------
                                                I. Jon Brumley
                                                Chairman and Chief Executive
                                                Officer


         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.

Note: The certification of the registrant furnished in this exhibit is not
deemed "filed" for purposes of Section 18 of the Securities and Exchange Act of
1934, as amended, or otherwise subject to the liabilities of that Section.
Registration Statements or other documents filed with the Securities and
Exchange Commission shall not incorporate this exhibit by reference, except as
otherwise expressly stated in such filing.