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


     The  undersigned  hereby  certify,  pursuant to 18 U.S.C.  Section 1350, as
adopted pursuant to Section 906 of the  Sarbanes-Oxley Act of 2002, that, to the
undersigned's  best knowledge and belief,  the Quarterly Report on Form 10-Q for
the Geodyne Energy Income  Limited  Partnership  II-H  ("Issuer") for the period
ending June 30, 2006 as filed with the Securities and Exchange Commission on the
date hereof (the "Report"):

      (a)   fully complies with the requirements of section 13(a) or 15(d) of
            the Securities Exchange Act of 1934; and
      (b)   the  information  contained in the Report  fairly  presents,  in all
            material respects, the financial condition and results of operations
            of the Issuer.

      Dated this 14th day of August, 2006.

                                    GEODYNE ENERGY INCOME LIMITED
                                    PARTNERSHIP II-H
                                    ("Issuer")

                                    //s// Dennis R. Neill
                                    -----------------------------------
                                    Dennis R. Neill
                                    President (Chief Executive Officer)

                                    //s// Craig D. Loseke
                                    -----------------------------------
                                    Craig D. Loseke
                                    Chief Accounting Officer
                                    (Chief Financial Officer)


      A signed  original of this written  statement  required by Section 906 has
been  furnished to Geodyne  Energy Income  Limited  Partnership II-H and will be
retained by Geodyne Energy Income Limited  Partnership II-H and furnished to the
Securities and Exchange Commission or its staff upon request.