Exhibit 99.1

NEWS RELEASE                                           Dorchester Minerals, L.P.

Release Date:  September 30, 2004                 3738 Oak Lawn Ave., Suite 300
                                                       Dallas, Texas 75219-4379
Contact:       Casey McManemin                                   (214) 559-0300

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

               DORCHESTER MINERALS, L.P. ANNOUNCES THE ACQUISITION
                 OF MINERAL AND ROYALTY PROPERTIES IN SIX STATES

     DALLAS, TEXAS  --  Dorchester Minerals, L.P. announced today the
Partnership's acquisition of oil and gas properties in exchange for the issuance
of 1.2 million common units of limited partnership interest. The properties
consist primarily of producing and nonproducing perpetual mineral and royalty
interests and are located in 104 counties and parishes in six states, including
producing interests in long-lived fields such as the Carthage Field in Panola
County, Texas, the McElroy Field in Upton County, Texas and the Knox Field in
Stephens County, Oklahoma. Oil and gas sales attributable to the properties
during the six month period ending June 30, 2004 were 12,000 bbls and 190,000
mcf, respectively.

     The seller is a private entity whose beneficiaries have generally owned the
properties for more than 50 years. The transaction is structured as a merger and
was sourced, negotiated and consummated without the assistance of an
intermediary.

     The  transaction is the Partnership's first acquisition of oil and gas
properties since its inception on January 31, 2003 and is consistent with its
stated objective of acquiring mineral and royalty interests in non-taxable
exchanges, utilizing the Partnership's units as consideration.

     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.

                                      -30-