Exhibit 31.15
                                  CERTIFICATION

I, Dennis R. Neill, certify that:

1.    I have reviewed  this Annual Report on Form 10-K of Geodyne  Energy Income
      Limited Partnership II-H;

2.    Based on my  knowledge,  this  annual  report  does not contain any untrue
      statement of a material fact or omit to state a material fact necessary to
      make the statements made, in light of the  circumstances  under which such
      statements were made, not misleading with respect to the period covered by
      this annual report;

3.    Based on my  knowledge,  the  financial  statements,  and other  financial
      information included in this annual report, fairly present in all material
      respects the financial condition,  results of operations and cash flows of
      the  registrant  as of, and for,  the  periods  presented  in this  annual
      report;

4.    The  registrant's  other  certifying  officer(s) and I are responsible for
      establishing  and  maintaining  disclosure  controls  and  procedures  (as
      defined in Exchange Act Rules  13a-15(e) and 15d-15(e)) for the registrant
      and have:

      (a)   Designed such  disclosure  controls and  procedures,  or caused such
            disclosure   controls  and  procedures  to  be  designed  under  our
            supervision,  to ensure that  material  information  relating to the
            registrant,  including its consolidated subsidiaries,  is made known
            to us by others  within  those  entities,  particularly  during  the
            period in which this annual report is being prepared;

      (b)   [Intentionally  omitted  per SEC's  transition  rules in SEC Release
            Nos. 33-8238 and 34-47986.];

      (c)   Evaluated the effectiveness of the registrant's  disclosure controls
            and procedures  and presented in this annual report our  conclusions
            about the  effectiveness of the disclosure  controls and procedures,
            as of the end of the period  covered by this annual  report based on
            such evaluation; and

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      (d)   Disclosed  in this  annual  report  any  change in the  registrant's
            internal  control over financial  reporting that occurred during the
            registrant's  most recent fiscal  quarter (the  registrant's  fourth
            fiscal  quarter in the case of an annual report) that has materially
            affected,   or  is  reasonably  likely  to  materially  affect,  the
            registrant's internal control over financial reporting; and

5.    The registrant's other certifying  officer(s) and I have disclosed,  based
      on  our  most  recent   evaluation  of  internal  control  over  financial
      reporting,  to the  registrant's  auditors and the audit  committee of the
      registrant's  board of directors  (or persons  performing  the  equivalent
      functions):

      (a)   All significant  deficiencies and material  weaknesses in the design
            or operation of internal control over financial  reporting which are
            reasonably  likely to adversely affect the  registrant's  ability to
            record, process, summarize and report financial information; and

      (b)   Any fraud,  whether or not  material,  that  involves  management or
            other  employees  who have a  significant  role in the  registrant's
            internal control over financial reporting.

Date:  March 19, 2004
                                        //S//Dennis R. Neill
                                    ----------------------------
                                    Dennis R. Neill, President
                                    (Principal Executive Officer)