UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549



                              ---------------------
                                    FORM 8-K
                            -------------------------

                                 CURRENT REPORT


     Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934

            Date of Report (Date of earliest event reported):  May 5, 2004
                                                              ------------



                            DORCHESTER MINERALS, L.P.
                            -------------------------
             (Exact name of Registrant as specified in its charter)



          Delaware                       000-50175              81-0551518
      -----------------                  ---------              ----------
(State or other jurisdiction of         Commission            (I.R.S. Employer
 incorporation or organization)         File Number          Identification No.)




        3738 Oak Lawn Avenue, Suite 300                            75219
                  Dallas, Texas                                  ---------
        -------------------------------                          (Zip Code)
(Address of principal executive offices)


       Registrant's telephone number, including area code:  (214) 559-0300
                                                            --------------

                                       N/A
                  ---------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)












Item 7.  Financial Statements and Exhibits.

(c)      Exhibits
         --------
         99.1     Press Release dated May 5, 2004 Announcing First
                  Quarter Results

Item 9.  Regulation FD Disclosure.

         See Item 12.  Results of Operations and Financial Condition.

Item 12. Results of Operations and Financial Condition.

         The Registrant is furnishing its press release dated May 5, 2004
which announces the Registrant's first quarter results. The press release is
attached hereto as Exhibit 99.1 and incorporated herein by reference.

         Limitation on Incorporation by Reference

         In accordance with general instructions B.2 and B.6 of Form 8-K, the
information in this report, including exhibits, is furnished pursuant to Items 9
and 12 and shall not be deemed "filed" for the purposes of Section 18 of the
Securities Exchange Act of 1934, or otherwise subject to the liability of that
section.






                                    SIGNATURE

         Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.


                                   DORCHESTER MINERALS, L.P.
                                   Registrant

                               by  Dorchester Minerals Management LP
                                   its General Partner,
                               by  Dorchester Minerals Management GP LLC
                                   its General Partner



Date: May 5, 2004              By: /s/ William Casey McManemin
                                  -----------------------------
                                   William Casey McManemin
                                   Chief Executive Officer





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

           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.

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