<ARTICLE> 5
<LEGEND>
THIS SCHEDULE CONTAINS SUMMARY FINANCIAL INFORMATION EXTRACTED FROM MESA
OFFSHORE TRUST 1998 SECOND QUARTER REPORT AND FORM 10-Q AND IS QUALIFIED IN ITS
ENTIRETY BY REFERENCE TO SUCH 1998 SECOND QUARTER REPORT AND FORM 10-Q.
</LEGEND>
       
                             
<PERIOD-TYPE>                   6-MOS
<FISCAL-YEAR-END>                          DEC-31-1998
<PERIOD-END>                               JUN-30-1998
<CASH>                                       2,296,382
<SECURITIES>                                         0
<RECEIVABLES>                                   27,824
<ALLOWANCES>                                         0
<INVENTORY>                                          0
<CURRENT-ASSETS>                                     0
<PP&E>                                     380,905,000
<DEPRECIATION>                             380,786,721
<TOTAL-ASSETS>                               2,442,485
<CURRENT-LIABILITIES>                        2,324,206
<BONDS>                                              0
<PREFERRED-MANDATORY>                                0
<PREFERRED>                                          0
<COMMON>                                             0
<OTHER-SE>                                     118,279
<TOTAL-LIABILITY-AND-EQUITY>                 2,442,485
<SALES>                                      1,135,274
<TOTAL-REVENUES>                             1,190,855
<CGS>                                                0
<TOTAL-COSTS>                                        0
<OTHER-EXPENSES>                               206,990
<LOSS-PROVISION>                                     0
<INTEREST-EXPENSE>                                   0
<INCOME-PRETAX>                                983,865
<INCOME-TAX>                                         0
<INCOME-CONTINUING>                            983,865
<DISCONTINUED>                                       0
<EXTRAORDINARY>                                      0
<CHANGES>                                            0
<NET-INCOME>                                   983,865
<EPS-PRIMARY>                                     0.01
<EPS-DILUTED>                                     0.01