Exhibit 99.1

NEWS RELEASE                                           Dorchester Minerals, L.P.

Release Date: April 19, 2005                       3838 Oak Lawn Ave., Suite 300
                                                        Dallas, Texas 75219-4379
Contact:  Casey McManemin                               Telephone (214) 559-0300
Facsimile (214) 559-0301

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       DORCHESTER MINERALS, L.P. ANNOUNCES ITS FIRST QUARTER DISTRIBUTION

        DALLAS, TEXAS -- Dorchester Minerals, L.P. announced today the
Partnership's first quarter 2005 cash distribution. The distribution of $.481242
per common unit represents activity for the three month period ending March 31,
2005 and is payable on May 9, 2005 to common unit holders of record as of
April 29, 2005.

        Cash receipts attributable to the Partnership's Net Profits Interests
during the first quarter totaled $6,498,000. These receipts generally reflect
oil and gas sales from the properties underlying the Net Profits Interests
during November 2004 through January 2005. The weighted average oil and gas
prices received for such sales were approximately $41.36/bbl and $6.16/mcf,
respectively. Approximately $585,000 of gross capital expenditures, primarily
attributable to drilling and completion activity, was paid by the owner of the
working interests in the properties underlying the Net Profits Interests during
December 2004 through February 2005. Cash receipts attributable to the
Partnership's Royalty Properties during the first quarter totaled $8,595,000.
These receipts generally reflect oil sales during December 2004 through February
2005 and gas sales during November 2004 through January 2005. The weighted
average oil and gas prices received for such sales were approximately $42.37/bbl
and $6.19/mcf, respectively.

        The Partnership received approximately $145,000 from lease bonus and
other sources during the first quarter and identified 74 new wells completed on
the Partnership's Net Profits Interests and Royalty Properties located in 33
counties and parishes in nine states.

        Dorchester Minerals, L.P. is a Dallas based owner of producing and
non-producing oil and natural gas mineral, royalty, overriding royalty, net
profits, and leasehold interests located in 25 states. 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.

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