EXHIBIT 3.10





AMENDED AND RESTATED



AGREEMENT OF LIMITED PARTNERSHIP



OF



DORCHESTER MINERALS OPERATING LP



Dated as of January 31, 2003



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THE PARTNERSHIP INTERESTS HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR THE SECURITIES LAWS OF ANY JURISDICTION. NO PARTNERSHIP INTEREST MAY BE SOLD OR OFFERED FOR SALE
(WITHIN THE MEANING OF ANY SECURITIES LAW) UNLESS A REGISTRATION STATEMENT UNDER ALL APPLICABLE SECURITIES LAWS WITH RESPECT TO THE INTEREST IS THEN IN EFFECT OR AN EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THOSE LAWS IS THEN APPLICABLE TO THE
INTEREST. A PARTNERSHIP INTEREST ALSO MAY NOT BE TRANSFERRED OR ENCUMBERED UNLESS THE APPLICABLE PROVISIONS OF THIS AGREEMENT ARE SATISFIED.



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AMENDED AND RESTATED

AGREEMENT OF LIMITED PARTNERSHIP

OF

DORCHESTER MINERALS OPERATING LP



THIS AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP of DORCHESTER MINERALS OPERATING LP (this
Agreement), dated as of January 31, 2003, is adopted, executed and agreed to by Dorchester Minerals Operating GP LLC, a Delaware limited liability company, as the sole general partner (the General Partner), and Dorchester
Minerals Management LP, a Delaware limited partnership, as the sole limited partner (the Limited Partner):



R E C I T A L S:



WHEREAS, effective December 12, 2001 the Certificate (as defined below) was filed in the office of the Secretary of State of Delaware for the formation of the Partnership (as defined below);



WHEREAS, in connection with the formation of the
Partnership, the General Partner and the Limited Partner executed that certain Agreement of Limited Partnership dated December 12, 2001 (the Original Agreement);



WHEREAS, the General Partner and the Limited Partner (i) have, pursuant to that certain letter agreement
dated January 22, 2003 (the Amendment), amended the Original Agreement and (ii) desire to amend and restate the Original Agreement in its entirety in this Agreement as of the date hereof to provide for the following terms and conditions
of the Original Agreement, as amended by the Amendment.



A G R E E M E N T:



NOW,
THEREFORE, for and in consideration of the mutual covenants and agreements herein set forth and intending to be legally bound, the parties hereto hereby enter into this Agreement pursuant to the provisions and upon the terms and conditions herein
contained, and hereby agree as follows:



ARTICLE I

DEFINITIONS



1.01 Definitions. As used in this Agreement, the following terms have the following meanings:



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Act means the Delaware Revised Uniform Limited Partnership Act, Title 6, Chapter 17 of the Delaware Code Annotated, as amended from time to time.



Agreement has the meaning given that term in the introductory paragraph.



Capital Contribution
means any contribution by a Partner to the capital of the Partnership.



Certificate has the meaning given that term in Section 2.01.



General Partner has the meaning given that term in the preamble hereto.



Limited Partner has the meaning
given that term in the preamble hereto.



Officer has the meaning given that term in Section 5.06.



Partner means the General Partner or the Limited Partner.



Partnership means Dorchester
Minerals Operating LP, a Delaware limited partnership.



Partnership Interest means the percentage ownership interest of a Partner in the Partnership. The initial Partnership Interest of the General Partner is one-tenth of one percent (0.10%), and the initial
Partnership Interest of the Limited Partner is ninety-nine and nine-tenths of one percent (99.90%).



Person has the meaning given that term in Section 101 of the Act.



Other terms defined herein have the meanings so given them.



1.02 Construction. Whenever the context
requires, the gender of all words used in this Agreement includes the masculine, feminine and neuter. All references to Articles and Sections refer to articles and sections of this Agreement. Terms used with initial capital letters will have the
meanings specified, applicable to both singular and plural forms, for all purposes of this Agreement. The word include (and any variation) is used in an illustrative sense rather than a limited sense. The word day means a calendar day.



ARTICLE II

ORGANIZATION



2.01 Formation. The Partnership has been formed as a Delaware limited partnership by the filing of a Certificate of Limited
Partnership (the Certificate) with the Delaware Secretary of States office under and pursuant to the Act.



2.02 Name. The name of the Partnership is Dorchester Minerals Operating LP and all Partnership business must be
conducted in that name or such other names that comply with applicable law as the General Partner may select from time to time.



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2.03
Registered Office; Registered Agent; Principal Office in the United States; Other Offices. The registered office of the Partnership required by the Act to be maintained in the State of Delaware shall be the office of the initial registered
agent named in the Certificate or such other office (which need not be a place of business of the Partnership) as the General Partner may designate from time to time in the manner provided by law. The registered agent of the Partnership in the State
of Delaware shall be the initial registered agent named in the Certificate or such other Person or Persons as the General Partner may designate from time to time in the manner provided by law. The principal office of the Partnership in the United
States shall be at such place as the General Partner may designate from time to time, which need not be in the State of Delaware. The initial principal office of the Partnership shall be at 3738 Oak Lawn Avenue, Suite 300, Dallas, Texas 75219. The
Partnership may have such other offices as the General Partner may designate from time to time.



2.04 Purpose. The business and purpose of the Partnership is to engage in such activities as the General Partner shall deem appropriate, to the extent such activities may be carried on under
applicable law and are not prohibited by the terms and provisions of this Agreement or the Act, including but not limited to, owning certain properties and providing accounting, land, tax and other operational support to the Limited Partner and to
Dorchester Minerals, Ltd., a Delaware limited partnership (Dorchester Minerals).



2.05 Powers. The Partnership shall have all of the powers necessary or convenient to achieve its purposes and to further its business and not restricted to it by law.



2.06 Legal Title. Legal title to the assets of the
Partnership will be taken and at all times held in the name of the Partnership.



2.07 Qualifications. The General Partner may take any and all actions deemed reasonably necessary by the General Partner to qualify the Partnership in foreign jurisdictions.



2.08 Mergers and Exchanges. With the consent of the
Partners, the Partnership may be a party to (a) a merger or (b) an exchange or acquisition of the type described in Section 201 of the Act.



2.09 Liability to Third Parties. Except as expressly provided in the Act, the Limited Partner shall not be liable for the debts,
obligations or liabilities of the Partnership, including under a judgment decree or order of a court.



2.10 Withdrawal of the Limited Partner. The Limited Partner may not withdraw from the Partnership prior to the dissolution and
winding up of the Partnership without the written consent of the General Partner.



2.11 Transfer or Pledge by a Partner. A Partner may transfer or pledge its Partnership Interest without restriction. The pledge or hypothecation of, or the granting of any security interest or
other lien or encumbrance against, all or part of a Partners interest in the Partnership by the Partner will not cause the withdrawal of the Partner from the Partnership.



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ARTICLE III

CAPITAL CONTRIBUTIONS



3.01 Initial and Additional Contributions. Each Partner has made an initial contribution to the capital of the Partnership as set
forth in the books and records of the Partnership. No Partner shall be required to make any additional contribution to the capital of the Partnership unless agreed to in writing by both Partners. Any agreement between the Partners for additional
capital contributions to the Partnership shall create rights and obligations only between the Partnership and the Partners, and shall not create any rights in any third party.



3.02 No Withdrawal of Contributions. A Partner shall not be entitled to withdraw any part of such
Partners capital account or to receive any distribution from the Partnership, except as specifically provided in this Agreement. There shall be no obligation to return to any Partner any part of such Partners capital contributions to the
Partnership until such time as the Partnership is dissolved and terminated.



3.03 Advances by a Partner. If the Partnership does not have sufficient cash to pay its obligations, a Partner may advance all or part of the needed funds to or on behalf of the Partnership. An
advance described in this Section constitutes a loan from the Partner to the Partnership, bears interest at a rate determined by the General Partner from the date of the advance until the date of payment, and is not a Capital Contribution.



ARTICLE IV

ALLOCATIONS AND DISTRIBUTIONS



4.01 Allocations. All items of income, gain, loss, deduction and credit of the Partnership shall be allocated to the Partners pro
rata in accordance with their Partnership Interests.



4.02 Distributions. Subject to the limitations of Section 607 of the Act and after the establishment of any reasonable reserve which the General Partner in good faith deems necessary for any contingent liabilities or
obligations of the Partnership, from time-to-time, as determined by the General Partner, all cash receipts of the Partnership, less the payment of expenses and the then due liabilities of the Partnership, shall be paid to the Partners pro rata in
accordance with their Partnership Interests. From time to time the General Partner also may cause assets of the Partnership other than cash to be distributed to the Partners, which distribution may be made subject to existing liabilities and
obligations and pro rata to the Partners in accordance with their Partnership Interests or upon such other basis as the Partners shall unanimously agree.



ARTICLE V

MANAGEMENT



5.01
Management. Subject to the provisions of this Agreement, the General Partner shall have exclusive authority to act on behalf of the Partnership. Subject to the provisions of



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this Agreement, the General Partner shall have the authority to manage the business and affairs of the Partnership. The Limited Partner shall
have no authority to participate in the management or act on behalf of or bind the Partnership. Notwithstanding anything to the contrary in this Agreement, the General Partner shall not cause the Partnership to sell or transfer any oil and gas
working interests owned by the Partnership and which underlie overriding royalty interests held by Dorchester Minerals, L.P. (the Operating ORRIs), unless the related Operating ORRIs are sold or transferred simultaneously by Dorchester
Minerals, L.P. at corresponding prices.



5.02
Removal of General Partner. The Limited Partner may remove the General Partner at any time, with or without cause, upon delivery to the General Partner at the principal office of the Partnership of written notice of such removal.



5.03 Compensation. The General Partner
shall not receive any compensation for its duties as General Partner.



5.04 No Voting Rights of Limited Partner. Except as specifically set forth in this Agreement or required by applicable law, the Limited Partner shall not have any voting, approval or consent rights.



5.05 Action by Written Consent. Whenever the approval
or consent of the Limited Partner is required or permitted hereunder or upon applicable law, such approval or consent shall take the form of a written consent executed by a duly authorized representative of the Limited Partner.



5.06 Officers. The General Partner may, from time to
time, designate one or more Persons to be officers of the Partnership (each, an Officer). No Officer need be a resident of the State of Delaware or a Partner. Any Officers so designated shall have such authority and perform such duties
as the General Partner may, from time to time, delegate to them. The General Partner may assign titles to particular Officers. Unless the General Partner decides otherwise, if the title is one commonly used for officers of a business corporation
formed under the Delaware General Corporation Law, the assignment of such title shall constitute the delegation to such Officer of the authority and duties that are normally associated with that office, subject to any specific delegation of
authority and duties made to such Officer by the General Partner pursuant to this Section 5.06. Each Officer shall hold office until his successor shall be duly designated and shall qualify or until his death or until he shall resign or shall have
been removed in the manner hereinafter provided. The same Person may hold any number of offices. The salaries or other compensation, if any, of the Officers and agents of the Partnership shall be fixed from time to time by the General Partner. Any
Officer may resign as such at any time. Such resignation shall be made in writing and shall take effect at the time specified therein, or if no time be specified, at the time of its receipt by the General Partner. The acceptance of a resignation
shall not be necessary to make it effective, unless expressly so provided in the resignation. Any Officer may be removed as such, either with or without cause, by the General Partner whenever in its judgment the best interest of the Partnership will
be served thereby; provided, however, that such removal shall be without prejudice to the contract rights, if any, of the Person so removed. Designation of an Officer shall not of itself create contract rights. The General Partner may fill any
vacancy occurring in any office of the Partnership. The Officers, to the extent of their powers set forth in this Agreement or otherwise vested in them by action of the



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General Partner, are agents of the Partnership for the purpose of conducting the business and affairs of the Partnership. The actions of any
Officer taken in accordance with such powers shall bind the Partnership and any third party dealing with such Officer shall be entitled to rely conclusively (without making inquiry of any kind) on any actions so taken as being properly authorized by
the Partnership.



ARTICLE VI

TAXES AND BOOKS



6.01 Federal Income Tax Treatment. For federal income tax purposes, the Partnership shall be disregarded as an entity separate from
the Partners pursuant to Treasury Regulations Section 301.7701-3(b)(1)(ii). The Partnership shall file no federal income tax returns.



6.02 Other Tax Returns. Subject to Section 6.01, the General Partner shall cause to be prepared and filed all necessary tax returns
for the Partnership.



6.03 Maintenance of
Books and Records. The Partnership shall keep accurate books and records relating to the assets of the Partnership in accordance with generally accepted accounting principles. The calendar year shall be the accounting year of the Partnership.
The Limited Partner shall be permitted access to all books and records of the Partnership at the principal office of the Partnership during business hours.



ARTICLE VII

DISSOLUTION, LIQUIDATION AND TERMINATION



7.01 Dissolution. The Partnership shall dissolve and its affairs shall be wound up on the first to occur of the following:



(a) The written consent of the Partners;



(b) The withdrawal of the General Partner or the occurrence of any other event that results
in the General Partner ceasing to be a General Partner, without the subsequent election of a successor general partner, which successor is hereby authorized to continue the business of the Partnership; or



(c) Entry of a decree of judicial dissolution
of the Partnership under Section 802 of the Act.



Upon an event described in Section 7.01(b), the Partnership thereafter shall be dissolved and liquidated unless within ninety (90) days of such event the Limited Partner agrees in writing to continue the business of the Partnership
and to the appointment of a successor general partner. If such election to continue the Partnership is made, then (i) the Partnership shall continue until another event causing dissolution in accordance with this Section 7.01 shall occur and (ii)
all necessary steps shall be taken to amend this Agreement to reflect the continuation of the business of the Partnership.



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The death,
retirement, resignation, expulsion, bankruptcy or dissolution of the Limited Partner or the occurrence of any other event that terminates the continued existence of the Limited Partner shall not cause the Partnership to be dissolved or its affairs
to be wound up.



The General Partner will not
cease to be a general partner of the Partnership or be deemed to have withdrawn from the Partnership as a result of the occurrence of an event described in Paragraphs (4) or (5) of Section 402(a) of the Act.



7.02 Liquidation and Termination. On dissolution of the
Partnership, the General Partner shall act as liquidating trustee or the Limited Partner may appoint one or more other Persons to act as liquidating trustee. The liquidating trustee shall proceed diligently to wind up the affairs of the Partnership
in accordance with Section 804 of the Act and make final distributions to the Partners pro rata in accordance with their Partnership Interests. The costs of liquidation shall be borne as a Partnership expense. Until final distribution, the
liquidating trustee shall continue to operate the Partnership assets with all of the power and authority of the General Partner.



7.03 Deficit Capital Accounts. Notwithstanding anything to the contrary contained in this Agreement, and notwithstanding any custom
or rule of law to the contrary, a Partner shall not be responsible for any deficit in any capital account attributed to such Partner, and upon dissolution of the Partnership any such deficit shall not be an asset of the Partnership and the Partner
shall not be obligated to contribute such amount to the Partnership to bring the balance of the Partners capital account to zero.



7.04 Certificate of Cancellation. On completion of the distribution of Partnership assets as provided herein, the Partnership is
terminated, and the General Partner (or such other Person or Persons as the Act may require or permit) shall file a Certificate of Cancellation with the Delaware Secretary of State and take such other actions as may be necessary to terminate the
Partnership.



ARTICLE VIII

GENERAL PROVISIONS



8.01 Entire Agreement; Supersedure. This Agreement constitutes the entire agreement of the Partners relating to the Partnership and
supersedes all prior contracts or agreements with respect to the internal governance of the Partnership, whether oral or written.



8.02 Effect of Waiver or Consent. A waiver or consent, express or implied, to or of any breach or default by any Person in the
performance by that Person of its obligations with respect to the Partnership is not a consent or waiver to or of any other breach or default in the performance by that Person of the same or any other obligations of that Person with respect to the
Partnership. Failure on the part of a Person to complain of any act of any Person or to declare any Person in default with respect to the Partnership, irrespective of how long that failure continues, does not constitute a waiver by that Person of
its rights with respect to that default until the applicable statute of limitations period has run.



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8.03
Amendment or Modification. This Agreement may be amended or modified from time to time only by a written instrument adopted by the Partners.



8.04 Binding Effect. This Agreement is binding on, and inures to the benefit of, the Partners and their heirs, legal
representatives, successors, and assigns.



8.05
Severability. If any provision of this Agreement or the application thereof to any Person or circumstance is held invalid or unenforceable to any extent, the remainder of this Agreement and the application of that provision to other Persons
or circumstances is not affected thereby and that provision shall be enforced to the greatest extent permitted by law.



8.06 Headings. Article and Section titles have been inserted for convenience of reference only, and they are not intended to affect
the meaning or interpretation of this Agreement.



8.07 Governing Law. THIS AGREEMENT IS GOVERNED BY AND SHALL BE CONSTRUED IN ACCORDANCE WITH THE LAW OF THE STATE OF DELAWARE, EXCLUDING ANY CONFLICT OF LAWS RULE OR PRINCIPLE THAT MIGHT REFER THE GOVERNANCE OR THE CONSTRUCTION
OF THIS AGREEMENT TO THE LAW OF ANOTHER JURISDICTION. In the event of a direct conflict between the provisions of this Agreement and (a) any provision of the Certificate or (b) any mandatory provision of the Act, the applicable provision of this
Agreement shall control except to the extent required by the Act.



(The next page is the signature page.)



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IN WITNESS
WHEREOF, the Partners have executed this Amended and Restated Agreement of Limited Partnership as of the date first set forth above.



GENERAL PARTNER:

DORCHESTER MINERALS OPERATING GP LLC,

a Delaware limited liability company



|By: |  | Its Sole Member:                   |  |                                       |  |                                                   
|--- |  | ---------------------------------- |  | ------------------------------------- |  | --------------------------------------------------
|    |  | DORCHESTER MINERALS MANAGEMENT LP, |  |                                       |  |                                                   
|    |  | a Delaware limited partnership     |  |                                       |  |                                                   
|   
|    |  | By:                                |  | Its General Partner                   |  |                                                   
|    |  |                                    |  | DORCHESTER MINERALS MANAGEMENT GP LLC |  |                                                   
|    |  |                                    |  | a Delaware limited liability company  |  |                                                   
|   
|    |  |                                    |  | By:                                   |  | /s/    JAMES E.
RALEY                             
|    |  |                                    |  |                                       |  | Name: James E. RaleyTitle: Chief Operating Officer



LIMITED PARTNER:

DORCHESTER MINERALS MANAGEMENT LP,

Delaware limited partnership



|By: |  | Its General Partner:                  
|--- |  | --------------------------------------
|    |  | DORCHESTER MINERALS MANAGEMENT GP LLC,
|    |  | a Delaware limited liability company  
|   
|    |  | By:                                   
|    |  |                                       



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