<DOCUMENT>
<TYPE>EX-99
<SEQUENCE>2
<FILENAME>dmlp080404_exh991.txt
<DESCRIPTION>DMLP 2004 2Q EARNINGS 8/4/04
<TEXT>
Exhibit 99.1


NEWS RELEASE                                           Dorchester Minerals, L.P.

Release Date:         August 4, 2004               3738 Oak Lawn Ave., Suite 300
                                                        Dallas, Texas 75219-4379
Contact:              Casey McManemin                             (214) 559-0300

--------------------------------------------------------------------------------



           DORCHESTER MINERALS, L.P. ANNOUNCES SECOND QUARTER RESULTS

        DALLAS, TEXAS -- Dorchester Minerals, L.P. (the "Partnership") announced
today the  Partnership's net earnings for the second quarter ended June 30, 2004
of $7,308,000, or $0.26 per common unit.

        A comparison of the Partnership's results for the three and six month
periods ending June 30, 2004 and 2003, are set forth below:

                             Three Months Ended           Six Months Ended
                                  June 30,                    June 30,
                        ---------------------------- ---------------------------
                        -------------- ------------- ------------- -------------
                              2004          2003          2004         2003
                         ------------- ------------- ------------- -------------
 Net Operating Revenues  $ 13,380,000  $ 11,300,000  $ 26,821,000  $ 25,256,000
 Depreciation, Depletion,
   Amortization            (5,022,000)   (6,672,000)  (10,323,000)  (11,643,000)
 Non-Cash Impairment                -   (22,214,000)            -   (22,214,000)
 All Other Expenses, Net   (1,050,000)   (1,342,000)   (2,539,000)   (6,384,000)
                         ------------- ------------- ------------- -------------
 Net Earnings (Loss)     $  7,308,000  $(18,928,000) $ 13,959,000  $(14,985,000)
                         ============= ============= ============= =============
 Net Earnings (Loss)
  Per Common Unit        $       0.26  $      (0.68) $       0.50  $      (0.60)


        The Partnership's net operating revenues during the three months ending
June 30, 2004 are higher than the same 2003 period primarily as a result of
increased crude oil and natural gas sales prices. Depreciation, depletion and
amortization decreased in 2004 compared to 2003 mainly as a result of a 2003
non-cash impairment which reduced the 2004 depletion basis. Net other expenses
decreased during the second quarter 2004 compared to 2003 due primarily to the
receipt of litigation settlements in 2004 and payment of organizational costs in
2003. Net earnings comparison of 2004 to 2003 periods are impacted by the 2003
non-cash impairment charge in accordance with full-cost accounting rules and by
January 2003 charges by a predecessor entity prior to the January 31, 2003
creation of the Partnership. 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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