<ARTICLE>                          5
<CIK>                              0000854062     
<NAME>                             GEODYNE ENERGY INCOME LTD PARTNERSHIP II-H
                                    
                                
<PERIOD-TYPE>                      3-MOS
<FISCAL-YEAR-END>                  DEC-31-1998
<PERIOD-START>                     JAN-01-1998
<PERIOD-END>                       MAR-31-1998
<CASH>                                   162,883
<SECURITIES>                                   0
<RECEIVABLES>                            187,397
<ALLOWANCES>                                   0
<INVENTORY>                                    0
<CURRENT-ASSETS>                         350,280
<PP&E>                                 5,990,503
<DEPRECIATION>                         4,811,311
<TOTAL-ASSETS>                         1,558,991
<CURRENT-LIABILITIES>                     33,306
<BONDS>                                        0
<PREFERRED-MANDATORY>                          0
<PREFERRED>                                    0
<COMMON>                                       0
<OTHER-SE>                             1,511,037
<TOTAL-LIABILITY-AND-EQUITY>           1,558,991
<SALES>                                  217,703
<TOTAL-REVENUES>                         277,956
<CGS>                                          0
<TOTAL-COSTS>                            136,457
<OTHER-EXPENSES>                               0
<LOSS-PROVISION>                               0
<INTEREST-EXPENSE>                             0
<INCOME-PRETAX>                          141,499
<INCOME-TAX>                                   0
<INCOME-CONTINUING>                      141,499
<DISCONTINUED>                                 0
<EXTRAORDINARY>                                0
<CHANGES>                                      0
<NET-INCOME>                             141,499
<EPS-PRIMARY>                               1.45
<EPS-DILUTED>                                  0