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):April 20, 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, 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 April 20, 2004 Announcing Cash
                  Distribution to Partners

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 April 20, 2004,
which announces the Registrant's quarterly distribution to partners. 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: April 20, 2004           By: /s/ William Casey McManemin
                                  -----------------------------
                                   William Casey McManemin
                                   Chief Executive Officer