CERTIFICATION

      I, Dennis R. Neill, certify that:

     I have reviewed this quarterly report on Form 10-Q of Geodyne Energy Income
Limited Partnership II-H;

     Based on my knowledge, this 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 report;

     Based on my  knowledge,  the  financial  statements,  and  other  financial
information included in this 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 report;

     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)) and internal  control over financial
reporting  (as defined in Exchange Act Rules  13a-15(f) and  15d-15(f))  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 quarterly 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 report our conclusions  about the effectiveness
of the disclosure  controls and procedures,  as of the end of the period covered
by this report based on such evaluation; and

     (d)  Disclosed  in this  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

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<PAGE>

     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 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.

      Dated this 14th day of May, 2004.


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

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