EXHIBIT 32.1


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER
                           AND CHIEF FINANCIAL OFFICER



         I, G. Steven Farris, certify that the Annual Report of Apache Offshore
Investment Partnership on Form 10-K for the year ended December 31, 2003, fully
complies with the requirements of Section 13(a) or 15(d) of the Securities
Exchange Act of 1934 (15 U.S.C. ss.78m or ss.78o (d)) and that information
contained in such report fairly represents, in all material respects, the
financial condition and results of operations of Apache Offshore Investment
Partnership.



/s/ G. Steven Farris
- -------------------------------------------
By:      G. Steven Farris
Title:   President, Chief Executive Officer
         and Chief Operating Officer of
         Apache Corporation, Managing Partner



         I, Roger B. Plank, certify that the Annual Report of Apache Offshore
Investment Partnership on Form 10-K for the year ended December 31, 2003, fully
complies with the requirements of Section 13(a) or 15(d) of the Securities
Exchange Act of 1934 (15 U.S.C. ss.78m or ss.78o (d)) and that information
contained in such report fairly represents, in all material respects, the
financial condition and results of operations of Apache Offshore Investment
Partnership.



/s/ Roger B. Plank
- -------------------------------------------
By:      Roger B. Plank
Title:   Executive Vice President
         and Chief Financial Officer of
         Apache Corporation, Managing Partner