U.S. SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                     FORM 3

            INITIAL STATEMENT OF BENEFICIAL OWNERSHIP OF SECURITIES

    Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934,
       Section 17(a) of the Public Utility Holding Company Act of 1935 or
               Section 30(f) of the Investment Company Act of 1940

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1.   Name and Address of Reporting Person*

Peak                                 Preston                 A.
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   (Last)                            (First)              (Middle)

3738 Oak Lawn Avenue, Suite 300
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                                    (Street)

Dallas                                  Texas                   75219
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   (City)                            (State)                (Zip)

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2.   Date of Event Requiring Statement (Month/Day/Year)

01/31/03
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3.   IRS Identification Number of Reporting Person, if an Entity (Voluntary)


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4.   Issuer Name and Ticker or Trading Symbol

Dorchester Minerals, L.P. (DMLP)
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5.   Relationship of Reporting Person to Issuer
     (Check all applicable)

     [X]  Director                             [_]  10% Owner
     [_]  Officer (give title below)           [_]  Other (specify below)

Manager
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6.   If Amendment, Date of Original (Month/Day/Year)

N/A
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7.   Individual or Joint/Group Filing  (Check applicable line)

     [X]  Form Filed by One Reporting Person

     [_]  Form Filed by More than One Reporting Person

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             Table I -- Non-Derivative Securities Beneficially Owned
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3. Ownership Form: 2. Amount of Securities Direct (D) or 1. Title of Security Beneficially Owned Indirect (I) 4. Nature of Indirect Beneficial Ownership (Instr. 4) (Instr. 4) (Instr. 5) (Instr. 4) - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ Common Units 358,486 I (1) - ------------------------------------------------------------------------------------------------------------------------------------ Common Units 72 I (2) - ------------------------------------------------------------------------------------------------------------------------------------ Common Units 142,396 I (3) - ------------------------------------------------------------------------------------------------------------------------------------ Common Units 1,075,458 I (4) - ------------------------------------------------------------------------------------------------------------------------------------ Common Units 1,000 I (5) - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ ====================================================================================================================================
* If the Form is filed by more than one Reporting Person, see Instruction 5(b)(v). Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly. (Print of Type Responses) (Over) FORM 3 (continued) Table II -- Derivative Securities Beneficially Owned (e.g., puts, calls, warrants, options, convertible securities) ================================================================================
5. Owner- 3. Title and Amount of Securities ship Underlying Derivative Security Form of 2. Date Exercisable (Instr. 4) Derivative and Expiration Date --------------------------------- 4. Conver- Security: (Month/Day/Year) Amount sion or Direct 6. Nature of ---------------------- or Exercise (D) or Indirect Date Expira- Number Price of Indirect Beneficial 1. Title of Derivative Exer- tion of Derivative (I) Ownership Security (Instr. 4) cisable Date Title Shares Security (Instr. 5) (Instr. 5) - ------------------------------------------------------------------------------------------------------------------------------------ No securities owned. - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ ====================================================================================================================================
Explanation of Responses: (1)Mr. Peak disclaims beneficial ownership of those common units owned by the Preston A. Peak FBO Martha Ann Peak Trust established for the benefit of his daughter. Mr. Peak is the trustee of the trust. (2) Mr. Peak disclaims beneficial ownership of those common units owned by the P A Peak Trust for Mary Lee Peak established for the benefit of daughter. Mr. Peak is the trustee of the trust. (3) The common units are held by 4MP Family Limited Partnership. Mr. Peak and his spouse are the beneficiaries of the Peak Revocable Living Trust and Mr. Peak is the trustee of the trust. The trust is the shareholder of 4MP Corp., which is the general partner of 4MP Family Limited Partnership. (4) The common units are held by 4MP Children's Limited Partnership. Mr. Peak and his spouse are the beneficiaries of the Peak Revocable Living Trust and Mr. Peak is the trustee of the trust, which is the shareholder of 4MP Corp., which is the general partner of 4MP Childrens Limited Partnership. (5) The common units are held by Hugoton Nominee, Inc. Mr. Peak and his spouse are the beneficiaries of the Peak Revocable Living Trust, which is the shareholder of Hugoton Nominee, Inc. /s/ Preston A. Peak 01/31/03 - --------------------------------------------- ----------------------- **Signature of Reporting Person Date ** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a). Note: File three copies of this form, one of which must be manually signed. If space provided is insufficient, see Instruction 6 for procedure. (Print of Type Responses) Page 2