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

Exhibit 99.1


NEWS RELEASE                                           Dorchester Minerals, L.P.
Release Date: April 20, 2004                       3738 Oak Lawn Ave., Suite 300
                                                        Dallas, Texas 75219-4379
Contact: Casey McManemin                                          (214) 559-0300
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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 2004 cash distribution. The distribution of $.415634
per common unit represents  activity for the three month period ending March 31,
2004 and is payable on May 10, 2004 to common unit holders of record as of April
30, 2004.

     Cash  receipts  attributable  to the  Partnership's  Net Profits  Interests
during the first quarter totaled  $6,062,000.  These receipts  generally reflect
oil and gas sales  from the  properties  underlying  the Net  Profits  Interests
during November and December 2003 and January 2004. The weighted average oil and
gas prices received for such sales were approximately  $27.36/bbl and $5.30/mcf,
respectively.  Approximately $185,000 of gross capital expenditures 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
2003  and  January  and  February  2004.  Cash  receipts   attributable  to  the
Partnership's  Royalty  Properties during the first quarter totaled  $6,122,000.
These receipts  generally reflect oil sales during December 2003 and January and
February 2004 and gas sales during  November and December 2003 and January 2004.
The  weighted   average  oil  and  gas  prices  received  for  such  sales  were
approximately $30.86/bbl and $4.54/mcf, respectively.

     The Partnership received  approximately $487,000 from lease bonus and other
sources during the first quarter,  and received division orders attributable to,
or otherwise identified, 44 new wells completed on the Partnership's Net Profits
Interests  and Royalty  Properties  located in 24 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 563  counties and parishes 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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