Exhibit 99.1

NEWS RELEASE                                          Dorchester Minerals, L.P.

Release Date: January 20, 2005                     3838 Oak Lawn Ave., Suite 300
                                                        Dallas, Texas 75219-4541
Contact:  Casey McManemin                               Telephone (214) 559-0300
                                                        Facsimile (214) 559-0301

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

     DALLAS, TEXAS  --  Dorchester Minerals, L.P. announced today the
Partnership's fourth quarter 2004 cash distribution. The distribution of
$.426076 per common unit represents activity for the three month period ending
December 31, 2004 and is payable on February 11, 2005 to common unit holders of
record as of February 1, 2005.

     Cash receipts attributable to the Partnership's Net Profits Interests
during the fourth quarter totaled $5,553,000. These receipts generally reflect
oil and gas sales from the properties underlying the Net Profits Interests
during August, September and October 2004. The weighted average oil and gas
prices received for such sales were approximately $41.88/bbl and $5.28/mcf,
respectively. Approximately $346,000 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
September, October and November 2004. Cash receipts attributable to the
Partnership's Royalty Properties during the fourth quarter totaled $8,217,000.
These receipts generally reflect oil sales during September, October and
November 2004 and gas sales during August, September and October 2004. The
weighted average oil and gas prices received for such sales were approximately
$41.88/bbl and $5.44/mcf, respectively.

     Fourth quarter results reflect payment of approximately $955,000 of ad
valorem taxes (partially offset by approximately $633,000 reserved in prior
quarters), and approximately $581,000 of nonrecurring expenses attributable to
Sarbanes-Oxley compliance matters, the relocation and consolidation of the
Partnership's offices, closing costs attributable to the transaction consummated
in the third quarter, advance severance tax payments made by the operating
partnership and reimbursed by the Partnership, and amounts paid in connection
with two small property acquisitions.

     The Partnership received approximately $259,000 from lease bonus and other
sources during the fourth quarter and identified 49 new wells completed on the
Partnership's Net Profits Interests and Royalty Properties located in 18
counties and parishes in seven 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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