<DOCUMENT>
<TYPE>EX-99
<SEQUENCE>2
<FILENAME>dmlp050404_exh991.txt
<DESCRIPTION>1Q 2004 EARNINGS FOR DMLP
<TEXT>
Exhibit 99.1


NEWS RELEASE                                           Dorchester Minerals, L.P.
Release Date: May 5, 2004                          3738 Oak Lawn Ave., Suite 300
                                                        Dallas, Texas 75219-4379
Contact: Casey McManemin                                          (214) 559-0300
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           DORCHESTER MINERALS, L.P. ANNOUNCES FIRST QUARTER RESULTS

     DALLAS,  TEXAS -- Dorchester Minerals,  L.P. (the "Partnership") announced
today the  Partnership's net earnings for the first quarter ended March 31, 2004
of $6,651,000, or $0.24 per common unit.

     A comparison of results for the periods ending March 31, 2003 and March 31,
2004 are set forth below:


                                                   Three Months Ended
                                                        March 31,
                                        ----------------------------------------
                                               2004                   2003
                                        ------------------     -----------------
Net Operating Revenues                     $  13,441,000          $  13,956,000
Depreciation, Depletion, Amortization         (5,301,000)            (4,971,000)
All Other Expenses                            (1,489,000)            (5,042,000)
Net Earnings                               $   6,651,000          $   3,943,000
                                        ------------------     -----------------
Earnings Per Common Unit                           $0.24                  $0.18
                                        ==================     =================
        In accordance with applicable accounting rules regarding the combination
ofthe business and properties of Dorchester Hugoton, Ltd., (Hugoton),
Republic Royalty Company (Republic) and Spinnaker Royalty Company (Spinnaker) on
January 31, 2003, Hugoton was deemed to be the acquiror of the Republic and
Spinnaker assets. Therefore, the first quarter 2003 results reflect Hugoton's
operations during January and the Partnership's operations during February and
March, and include severance (employee retention) payments and other payments
made by Hugoton immediately prior to the combination transaction. The
Partnership's cash distributions are not comparable to its net earnings due to
timing and other differences including depletion.

     Dorchester  Minerals,  L.P. is a Dallas area based owner of  producing  and
non-producing crude oil and natural gas mineral, royalty, overriding royalty,
net profits,  and  leasehold  interests and its common units trade on the Nasdaq
Stock Market under the symbol DMLP.

FORWARD-LOOKING STATEMENTS

Portions of this document may constitute "forward-looking statements" as
defined by federal law. Such statements are subject to certain risks,
uncertainties and assumptions. Should one or more of these risks or
uncertainties materialize, or should underlying assumptions prove incorrect,
actual results may vary materially from those anticipated, estimated or
projected. Examples of such uncertainties and risk factors include, but are not
limited to, changes in the price or demand for oil and natural gas, changes in
the operations on or development of the Partnership's properties, changes in
economic and industry conditions and changes in regulatory requirements
(including changes in environmental requirements) and the Partnership's
financial position, business strategy and other plans and objectives for future
operations. These and other factors are set forth in the Partnership's filings
with the Securities and Exchange Commission.

                                      -30-

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