<ARTICLE> 5
<LEGEND>
THIS SCHEDULE CONTAINS SUMMARY FINANCIAL INFORMATION EXTRACTED FROM MESA ROYALTY
TRUST 1998 THIRD QUARTER REPORT AND FORM 10-Q AND IS QUALIFIED IN ITS ENTIRETY
BY REFERENCE TO SUCH 1998 THIRD QUARTER REPORT AND FORM 10-Q.
</LEGEND>
       
                             
<PERIOD-TYPE>                   9-MOS
<FISCAL-YEAR-END>                          DEC-31-1998
<PERIOD-END>                               SEP-30-1998
<CASH>                                       1,395,658
<SECURITIES>                                         0
<RECEIVABLES>                                   17,005
<ALLOWANCES>                                         0
<INVENTORY>                                          0
<CURRENT-ASSETS>                             1,412,663
<PP&E>                                      42,498,034
<DEPRECIATION>                              28,189,748
<TOTAL-ASSETS>                              15,720,949
<CURRENT-LIABILITIES>                        1,412,663
<BONDS>                                              0
<PREFERRED-MANDATORY>                                0
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<COMMON>                                             0
<OTHER-SE>                                  14,308,286
<TOTAL-LIABILITY-AND-EQUITY>                15,720,949
<SALES>                                      5,203,701
<TOTAL-REVENUES>                             5,266,579
<CGS>                                                0
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<INTEREST-EXPENSE>                                   0
<INCOME-PRETAX>                              5,235,250
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<NET-INCOME>                                 5,235,250
<EPS-PRIMARY>                                     2.81
<EPS-DILUTED>                                     2.81