<PAGE>   1
                                                                     EXHIBIT 4.3

                               NOMINEE AGREEMENT

         THIS NOMINEE AGREEMENT is made and entered into effective as of the
19th day of August, 1982 by and among Dorchester Gas Corporation, a Delaware
corporation ("Dorchester"), Dorchester Hugoton, Ltd., a Texas limited
partnership (the "Partnership") and Hugoton Nominee, Inc., a Texas corporation
("Nominee").

         WHEREAS, the Partnership is a limited partnership created and existing
pursuant to a Certificate and Agreement of Limited Partnership filed with the
Secretary of State of Texas on June 17, 1982 (as now in effect or as hereafter
amended, the "Partnership Agreement"), with George S. Rooker, Preston A. Peak,
and John R. Barnes, as initial General Partners, and Dorchester as the initial
Limited Partner;

         WHEREAS, Dorchester has assigned all of the units of limited
partnership interest ("Units") of the Partnership to the holders of Dorchester
Common Stock of record at the close of business on July 2, 1982 and to certain
key employees (collectively, the "Distributees");

         WHEREAS, pursuant to a Depositary Agreement dated as of June 17, 1982
among Mercantile National Bank at Dallas (the "Depositary"), Dorchester and the
Partnership (as now in effect or as hereafter amended, the "Depositary
Agreement"), Dorchester has deposited Certificate No. 1 evidencing the Units
with the Depositary and directed the Depositary to issue depositary receipts
("Depositary Receipts") evidencing the Units to the Distributees; and

         WHEREAS, it is necessary to provide a nominee to act as a limited
partner of record for those recipients and holders from time to time of
Depositary Receipts who do not elect to become substituted Limited Partners
under the Partnership Agreement and applicable state law.

         NOW, THEREFORE, in consideration of the premises and promises
hereinafter contained, it is agreed by and among the parties hereto as follows:

         1.  Definitions. Unless the context otherwise requires, terms not
otherwise defined herein shall have the meaning given them in the Partnership
Agreement.

         2.  Substitution as Limited Partner of Record. Nominee agrees to
become a substituted Limited Partner in the Partnership subject to the
provisions of this Agreement and to the right of recipients and holders from
time to time of Depositary Receipts to become substituted Limited Partners in
accordance with the terms of the Depositary Agreement and the Partnership
Agreement. The parties hereto shall execute and deliver such documents and take
such actions as may be necessary or appropriate to evidence or consent to the
substitution herein contemplated. It is understood, acknowledged and agreed
that (i) Nominee is becoming a substituted Limited Partner for the limited
purpose of being reflected as a nominee limited partner under the Partnership
Agreement and applicable state law, and (ii) all rights and interests of
Dorchester, as the
<PAGE>   2
initial Limited Partner, including the right to become a substitute Limited
Partner, have been assigned by Dorchester to the Distributees. Consistent with
the foregoing, Nominee agrees to execute and deliver such documents and take
such actions from time to time as may be necessary or appropriate to provide
for the admission of holders of Depositary Receipts as substituted Limited
Partners in accordance with the provisions of the Partnership Agreement and
applicable state law.

         3.      Exercise of Rights as a Limited Partner.
                 ---------------------------------------

                 (a)      Nominee shall have no obligation to exercise any
rights it may have as a Limited Partner of record. To the extent Nominee
exercises any residual rights and powers remaining in Nominee as a Limited
Partner of record, Nominee agrees to use its best efforts to exercise such
rights and powers in favor and in the best interests of the record holders of
Depositary Receipts representing the Units with respect to which Nominee is the
record Limited partner.

                 (b)      With respect to those Units held of record by Nominee
from time to time, Nominee hereby irrevocably designates the record holder of
the Depositary Receipt(s) evidencing such Units as its representative for
purposes of exercising the right of a Limited Partner to inspect the books and
records of the Partnership in accordance with the provisions of the Partnership
Agreement and applicable state law. Nominee agrees to furnish or cause to be
furnished to each such record holder of a Depositary Receipt all notices,
reports, communications and information delivered to Nominee, in its capacity
as a Limited Partner of record, under the Partnership Agreement; provided,
however, if such notices, reports, communications and information are otherwise
furnished to such Depositary Receipt record holders, Nominee shall have no
obligation to additionally furnish such notices, reports, communications and
information.  In connection with any notice received by Nominee as a Limited
Partner to vote under the Partnership Agreement or applicable law, Nominee
agrees to inform, directly or indirectly, such record holders of their right to
become substituted Limited Partners.

         4.      Reimbursement for Expenses and Indemnification.
                 ----------------------------------------------

                 (a)      The Partnership agrees to reimburse Nominee for all
expenses incurred by Nominee in its capacity as Limited Partner of record under
this Agreement.

                 (b)      In any threatened, pending or completed action, suit
or proceeding to which Nominee was or is a party, or is threatened to be made a
party, by reason of the fact that it is or was a Limited Partner of the
Partnership, the Partnership agrees to indemnify Nominee against, and hold it
harmless from, any liability incurred by Nominee in such capacity if, in the
transaction giving rise to such action, suit or proceeding, Nominee acted in
good




                                     -2-
<PAGE>   3
faith and in a manner it reasonably believed to be in, or not opposed to, the
best interests of the Partnership and Nominee's conduct in such transaction did
not constitute gross negligence, intentional misconduct or willful breach of
Nominee's obligations under this Agreement. The indemnification and immunities
provided for in this paragraph shall extend to Nominee's officers, directors,
shareholders, employees and agents.

         5.      Resignation and Removal.

                 (a)      Nominee may at any time resign as a Limited Partner
of record under this Agreement by written notice of its election to do so
delivered to the Partnership. Such resignation shall take effect upon the
appointment and substitution of a successor Limited Partner of record and its
acceptance of such appointment as hereinafter provided.

                 (b)      Nominee may at any time be removed by the Partnership
as a Limited Partner of record under this Agreement by written notice of
removal delivered to Nominee, such removal to be effective upon the appointment
and substitution of a successor Limited Partner of record under this Agreement
and its acceptance of such appointment as hereinafter provided.

                 (c)      If Nominee resigns or is removed, the Partnership
shall, within thirty (30) days after the delivery of the notice of resignation
or removal, as the case may be, appoint a successor Limited Partner of record
to act under this Agreement. Any successor Limited Partner of record under this
Agreement shall execute and deliver to its predecessor and to the Partnership
an instrument in writing accepting its appointment, and thereupon such
successor Limited Partner, without any further act or deed, shall become fully
vested with all the rights, powers, duties and obligations of its predecessor.
The predecessor, upon the written request of the Partnership, shall execute and
deliver an instrument transferring to the successor Limited Partner all rights
and powers of the predecessor under this Agreement and shall take such other
action as may be necessary or appropriate to effect or evidence such
succession. If Nominee resigns or is removed, it shall, if requested by the
Partnership, promptly change its name so as to reflect that it no longer is
acting as a Limited Partner of record under this Agreement or otherwise
associated with the Partnership. In the event the Partnership requests such
name change, Nominee shall permit its successor hereunder to utilize the name
"Hugoton Nominee, Inc." and shall execute and deliver such documents and take
such actions as may be necessary or appropriate to permit such use.

         6.      Amendment. This Agreement may at any time and from time to
time be amended by agreement among the parties hereto in any respect deemed
necessary or desirable by them that does not adversely affect any substantial
right of the record holders of Depositary Receipts for Units held of record by
Nominee. Any amendment of this Agreement that adversely affects any substantial




                                     -3-
<PAGE>   4
right of the record holders of Depositary Receipts for Units held of record by
Nominee shall be approved by the record holders of Depositary Receipts
evidencing the Applicable Percentage Interest of such Units.

         7.      Termination. This Agreement shall terminate upon the earlier
of (i) the failure of Nominee to hold any Units of record as a Limited Partner
under this Agreement or (ii) dissolution of the Partnership (subject to
reconstitution in certain events) as provided in the Partnership Agreement.

         8.      Successors and Assigns. This Agreement shall be binding upon
the parties hereto and their respective successors and assigns, and shall
inure to the benefit of said parties, their successors and permitted assigns.
Nominee shall not be entitled to assign any of its rights under this Agreement
without first obtaining the written consent of the other parties hereto.

         9.      Invalid Provisions. If any provision of this Agreement is held
to be illegal, invalid or unenforceable under present or future laws, such
provision shall be fully severable; this Agreement shall be construed and
enforced as if such illegal, invalid or unenforceable provision had never
comprised a part hereof; the remaining provisions of the Agreement shall remain
in full force and effect and shall not be affected by the illegal, invalid or
unenforceable provision; and it is the intent of each party hereto that there
shall be added automatically as a part of the Agreement, a provision (prepared
by counsel for the Partnership) as similar in terms to such illegal, invalid or
unenforceable provision as may be possible and be legal, valid and enforceable.

         10.     Governing Law. This Agreement is entered into and shall be
construed and enforced in accordance with the applicable laws of the State of
Texas.

         11.     Counterparts. This Agreement may be executed in several
counterparts and by the several parties hereto, on separate counterparts, and
each counterpart, when executed and delivered, shall constitute an original
instrument, and all such separate counterparts shall constitute but one and the
same agreement.

         11.     Notices. All notices or other communications required or
permitted to be given pursuant to this Agreement shall be in writing and shall
be considered as properly given or made if hand delivered or mailed from within
the United States by first class United States mail, postage prepaid, or by
pre-paid telegram or telex and addressed to each party at its address as set
out on the signature pages to this Agreement. Any party may change its address
by giving a notice in writing to the other parties stating its new address.




                                     -4-
<PAGE>   5
         IN WITNESS WHEREOF, this Agreement has been executed as of the day and
year first above written by the parties hereto.


                                        DORCHESTER GAS CORPORATION
                                        5735 Pineland Drive
                                        P.O. Box 31049
                                        Dallas, Texas 75231
                                        
                                        By: /s/ GEORGE S. ROOKER
                                            ------------------------------
                                            George S. Rooker, Chairman of
                                            the Board
                                        
                                        
                                        DORCHESTER HUGOTON, LTD.
                                        5735 Pineland Drive
                                        Suite 129
                                        Dallas, Texas 75231
                                        
                                        By: /s/ PRESTON A. PEAK
                                            ------------------------------
                                            Preston A. Peak, Authorized
                                            General Partner
                                        
                                        
                                        HUGOTON NOMINEE, INC.
                                        5735 Pineland Drive
                                        Suite 129
                                        Dallas, Texas 75231
                                        
                                        By: /s/ HOWARD C. WADSWORTH
                                            ------------------------------
                                            Howard C. Wadsworth
                                            President
                                        



                                     -5-