EXHIBIT 10.2

                            ALLIANCE RESOURCES PLC

                         REGISTRATION RIGHTS AGREEMENT

     This REGISTRATION RIGHTS AGREEMENT dated as of October 30, 1998 (this
"AGREEMENT") by and between ALLIANCE RESOURCES PLC, a public limited company
organized under the laws of England and Wales (the "COMPANY"), ENCAP EQUITY 1996
LIMITED PARTNERSHIP, a Texas limited partnership ("ENCAP LP"), ENERGY CAPITAL
INVESTMENT COMPANY PLC, an English investment company ("ECIC"), and ENCAP
INVESTMENTS L.C., a Texas limited liability company ("ENCAP LC") (with EnCap LP,
ECIC and EnCap LC being herein collectively called the "NEW SHAREHOLDERS");

                                   RECITALS:

     A.   The Company and the New Shareholders are parties to that certain
Purchase Agreement dated as of October 27, 1998 (the "PURCHASE AGREEMENT").

     B.   The ability of the New Shareholders to freely trade the ordinary
shares, 1p per share, of the Company (the "Ordinary Shares") received by the New
Shareholders pursuant to the Purchase Agreement may be limited by applicable
federal securities laws.

     C.   In order to improve the transferability of the Ordinary Shares to be
received by the Stockholder pursuant to the Purchase Agreement, the New
Shareholders have requested the Company to provide to the New Shareholders
limited registration rights with respect to the Ordinary Shares to be received
by the New Shareholders pursuant to the Purchase Agreement, and the Company has
agreed to provide such rights on the terms and subject to the conditions herein.

     D.   The execution and delivery of this Agreement by the Company is a
condition to the obligation of the New Shareholders to consummate the
transactions contemplated by the Purchase Agreement.

                                  AGREEMENT:

     NOW, THEREFORE, in consideration of the premises and the mutual agreements
herein set forth and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto, intending to
be legally bound, hereby agree as follows:

                                   ARTICLE I

                              REGISTRATION RIGHTS

     The Company and the New Shareholders covenant and agree as follows:

 
     SECTION 1.  DEFINITIONS AND REFERENCES.

     (a) When used in this Agreement, the following terms shall have the
respective meanings assigned to them in this Section 1 or in the sections,
subsections or other subdivisions referred to below:

     "AGREEMENT" shall mean this Agreement, as hereafter changed, modified or
amended in accordance with the terms hereof.

     "COMMISSION" shall mean the Securities and Exchange Commission (or any
successor body thereto).

     "COMPANY" shall have the meaning assigned to it in the introductory
paragraph hereof.
 
     "CLOSING DATE" shall have the meaning assigned to in the Purchase
Agreement.

     "DEMAND REGISTRATION" shall have the meaning assigned to it in Section
2(a).

     "DIFCO AGREEMENT" shall mean that certain Registration Rights Agreement
dated as of October 30, 1998, among the Company and F. Fox Benton and certain
members of his family.

     "DIFCO HOLDERS" shall mean those persons identified as Selling Shareholders
in the Difco Agreement.

     "ECIC" shall have the meaning assigned to it in the introductory paragraph
hereof.

     "ENCAP LP" shall have the meaning assigned to it in the introductory
paragraph hereof.

     "ENCAP LC" shall have the meaning assigned to it in the introductory
paragraph hereof.

     "EXCHANGE ACT" shall mean the Securities Exchange Act of 1934, as amended,
and all rules and regulations promulgated under such Act.
 
     "HOLDER" shall mean any Person that holds Registrable Securities.

     "HOLDER INDEMNIFIED PARTIES" shall have the meaning assigned to it in
Section 9(a).

     "LASALLE AGREEMENT" shall mean that certain Registration Rights Agreement
dated as of October 30, 1998, among the Company and LaSalle.

     "LASALLE" shall mean LaSalle Street Natural Resources Corporation, as a
party to the LaSalle Agreement.

     "NEW SHAREHOLDERS" shall have the meaning assigned to it in the
introductory paragraph hereof.

                                      -2-

 
     "ORDINARY SHARES" shall have the meaning assigned to in Paragraph B of the
Recitals hereto.

     "PERSON" shall mean any individual, corporation, partnership, joint
venture, limited partnership, limited liability company, trust, unincorporated
organization or government or any agency or political subdivision thereof.

     "PIGGYBACK REGISTRATION" shall have the meaning assigned to it in Section
3.

     "PURCHASE AGREEMENT" shall have the meaning assigned to in  Paragraph A of
the Recitals hereto.

     "REGISTRABLE SECURITIES" shall mean (i) the Ordinary Shares received by the
New Shareholders pursuant to the Purchase Agreement and (ii) any securities
issued or issuable with respect to the shares described in clause (i) above by
way of a stock dividend or stock split or in connection with a combination of
shares, recapitalization, merger, consolidation or other reorganization.

     "REGISTRATION EXPENSES" shall mean all expenses incident to the Company's
performance of or compliance with the registration rights granted hereunder,
including (without limitation) all registration and filing fees, fees and
expenses of compliance with securities and blue sky laws, printing and engraving
expenses, messenger, telephone and delivery expenses, and fees and disbursements
of counsel for the Company, all independent certified public accountants and
underwriters (excluding discounts and commissions) and the reasonable fees and
expenses of one counsel to such New Shareholders as a group; provided, that
Registration Expenses shall not include any Selling Expenses.

     "SECURITIES ACT" shall mean the Securities Act of 1933, as amended, and all
rules and regulations under such Act.

     "SELLING EXPENSES" shall mean underwriting discounts or commissions, any
selling commissions and stock transfer taxes attributable to sales of
Registrable Securities.

     (b) All references in this Agreement to sections, subsections and other
subdivisions refer to corresponding sections, subsections and other subdivisions
of this Agreement unless expressly provided otherwise.  Titles appearing at the
beginning of any of such subdivisions are for convenience only and shall not
constitute part of such subdivisions and shall be disregarded in construing the
language contained herein.  The words "this Agreement", "this instrument",
"herein", "hereof", "hereby", "hereunder" and words of similar import refer to
this Agreement as a whole and not to any particular subdivision unless expressly
so limited.  Words in the singular form shall be construed to include the plural
and vice versa, unless the context otherwise requires.  Pronouns in masculine,
feminine and neuter genders shall be construed to include any other gender.

     SECTION 2.  DEMAND REGISTRATION RIGHTS.

     (a) At any time after the Closing Date, a Holder may request  a
registration by the Company under the Securities Act of all or a part its
Registrable Securities (a "DEMAND REGISTRATION").

                                      -3-

 
     (b) Notwithstanding subsection (a) above or anything else herein to the
contrary, the Company shall not be obligated to effect more than two
registrations pursuant to this Section 2; provided, however, that any
registration requested pursuant to this Section 2 will not be deemed to have
been effected (i) unless it has become effective and remained effective for the
lesser of either the period necessary to complete the sale or disposition of the
Registrable Securities covered by such registration statement or one year, (ii)
if, after it has become effective, such registration is terminated by a stop
order, injunction or other order of the Commission or other governmental agency
or court or (iii) is withdrawn at the request of the Holders after the
registration statement has been filed with the Commission.

     (c) Notwithstanding subsection (a) above or anything else herein to the
contrary, it is hereby agreed that a Demand Registration must cover no less than
50% of the Registrable Securities held by the Holders then outstanding.  In the
event a Demand Registration is requested pursuant to this Section 2, the Company
will (i) promptly give notice of the proposed registration to any other New
Shareholder not making the request, if any, and (ii) use its reasonable best
efforts to effect the registration of the Registrable Securities specified in
the request, together with the Registrable Securities of any other New
Shareholder joining in such request as are specified in a written request
received by the Company within 20 days after receipt of the notice referred to
in clause (i) above.

     (d) A registration statement filed under this Section 2 pursuant to the
request of Holders of Registrable Securities may include other securities of the
Company, with respect to which "piggyback" registration rights have been
granted, and may include securities of the Company being sold for the account of
the Company; provided, however, that if the Company shall request inclusion in
any registration pursuant to this Section 2 of the securities being sold for its
own account, or if other persons shall request inclusion in any registration
pursuant to this Section 2, the New Shareholders shall offer to include such
securities in the offering and may condition such offer on their acceptance of
any other reasonable conditions (including, without limitation, if such offering
is underwritten, that such requesting holders agree in writing to enter into an
underwriting agreement with usual and customary terms).  Notwithstanding any
other provisions of this Section 2, if the representative of the underwriters
advises the Holders of Registrable Securities in writing that marketing factors
require a limitation on the number of shares to be underwritten, the number of
shares to be included in the underwriting or registration shall be allocated
first to the Holders of Registrable Securities, the Difco Holders and LaSalle
(pro rata, based on the number of Registrable Securities requested by each such
holder to be included therein), second to the Company and thereafter to any
other holders requesting inclusion in the registration on the basis of the
number of shares each other requesting holder requests be included bears to the
total number of shares of all other requesting holders that have been requested
be included in such registration.  If a person who has requested inclusion in
such registration as provided above does not agree to the terms of any such
underwriting, such person shall be excluded therefrom by written notice from the
Company, the underwriter, or the Holders of Registrable Securities.  The
securities so excluded shall also be withdrawn from registration.

     SECTION 3.  PIGGYBACK REGISTRATION RIGHTS.

     (A) If the Company proposes to register any of its securities under the
Securities Act other than (i) under employee compensation or benefit programs,
(ii) pursuant to an exchange offer or an offering of securities solely to the
existing stockholders or employees of the Company, or (iii) 

                                      -4-

 
securities to be issued in connection with an acquisition or a transaction
described in Rule 145(a) promulgated under the Securities Act, and the
registration form to be used may be used for the registration of Registrable
Securities, the Company will give prompt written notice (which, in any event,
shall be given no less than 15 days prior to the filing of a registration
statement with respect to such offering) to Holders of Registrable Securities of
its intention to effect such a registration and, upon the written request of a
Holder of Registrable Securities sent within 15 days after the effective date of
any such notice, the Company will use its best efforts to cause all Registrable
Securities as to which any Holder shall have so requested registration to be
registered under the Securities Act, all to the extent necessary to permit the
sale in such offering of the Registrable Securities so registered on behalf of
such Holder in the same manner as the Company (or stockholder other than such
Holder, as the case may be) proposes to offer its securities (a "PIGGYBACK
REGISTRATION"). The Company shall use its best efforts to cause the managing
underwriter or underwriters of a proposed underwritten offering to permit the
Registrable Securities requested by a Holder to be included in the registration
for such offering on the same terms and conditions as any similar securities of
the Company included therein; provided, however, that (A) if, at any time after
giving written notice of its intention to register any of its securities and
before the effective date of the registration statement filed in connection with
the registration, the Company determines for any reason not to register its
securities, the Company may, at its election, give written notice of its
determination to the Holders of Registrable Securities and, thereupon, shall be
relieved of its obligation to register any Registrable Securities in connection
with that registration, without prejudice, however, to the future rights of the
Holders of Registrable Securities under this Section, (B) if the Company
determines in its discretion to delay the registration of its securities, the
Company shall be permitted to delay the registration of any Registrable
Securities for the same period as the delay in registering any other securities,
and (C) the Company is not required to effect any registration for a requesting
Holder of Registrable Securities pursuant to this Section 3 unless it receives
reasonable assurances that the requesting Holder of Registrable Securities will
pay any expenses required to be paid by it as provided in Section 5.

     (b) If a Piggyback Registration is an underwritten registration and the
managing underwriter(s) for the offering advises the Company in writing that in
its opinion the number of shares of Registrable Securities requested or proposed
to be included in the registration exceeds the number that can be sold in the
offering without materially affecting the offering price of the securities
proposed to be included in the offering, then the number of securities to be
offered for the account of any participating Holder(s) shall be reduced pro rata
based upon the number of securities proposed to be sold by the Company, such
Holder(s) and other Persons to the extent necessary to reduce the total number
of securities to be included in such offering to the number of shares
recommended by such managing underwriter; provided, however, that if securities
of the Company are being offered for the account of other Persons as well as the
Company, such reduction shall first be made from the securities intended to be
offered by such Persons other than the participating Holder(s), the Difco
Holders and LaSalle.

     (c) If any Piggyback Registration is an underwritten offering, the Company
will have the sole right to select the managing underwriter(s) thereof.

     (d) The rights of the Holders with respect to Piggyback Registrations shall
be pari passu wit the piggyback registration rights of the Difco Holders and
LaSalle.

                                      -5-

 
     SECTION 4.  REGISTRATION PROCEDURES.

     (a) Whenever the Holders of Registrable Securities have requested that any
Registrable Securities be registered pursuant to Section 2 or Section 3, the
Company will as expeditiously as possible:

          (i)   prepare and file with the Commission a registration statement on
     the appropriate form with respect to such Registrable Securities, and use
     its reasonable best efforts to cause such registration statement to become
     effective as soon as reasonably practicable after the filing thereof;
     provided, however, that the Company may discontinue any registration of
     securities that is being effected pursuant to Section 3 at any time prior
     to the effective date of the registration statement relating thereto, and
     provided further, that before filing a registration statement or prospectus
     or any amendments or supplements thereto, including documents incorporated
     by reference after the initial filing of any registration statement, as
     soon as practicable, the Company will furnish to any Holder covered by such
     Registration Statement copies of all such documents proposed to be filed,
     which documents will be subject to the review of such Holder;

          (ii)  prepare and file with the Commission such amendments and
     supplements to such registration statement and the prospectus used in
     connection therewith as may be necessary to keep such registration
     statement effective for a period of not less than the period set forth in
     such section or such shorter period which will terminate when Registrable
     Securities covered by such registration statement have been sold (but not
     before the expiration of the applicable prospectus delivery period) and
     comply with the provisions of the Securities Act with respect to the
     disposition of all securities covered by such registration statement during
     such period in accordance with the intended methods of disposition by the
     sellers thereof set forth in such registration statement;

          (iii) notify each seller of Registrable Securities requesting
     registration, promptly after the Company shall receive notice thereof, of
     the time when such registration statement has been filed;

          (iv)  furnish without charge to each seller of Registrable Securities
     such number of copies of such registration statement, each amendment and
     supplement thereto, including financial statements and schedules, all
     documents incorporated therein by reference and all exhibits (including
     those incorporated by reference); the prospectus included in such
     registration statement (including, without limitation, each preliminary
     prospectus); and such other documents as such seller may reasonably request
     in order to facilitate the disposition of the Registrable Securities owned
     by such seller;

          (v)   use its reasonable best efforts to register or qualify such
     Registrable Securities under such other securities or blue sky laws of such
     jurisdictions within the United States as any seller reasonably requests;
     keep each such registration or qualification effective during the period
     such registration statement is required to be kept effective; and do any
     and all other acts and things which may be reasonably necessary or
     advisable to enable such seller to consummate the disposition in such
     jurisdictions of the Registrable Securities owned by such 

                                      -6-

 
     seller (provided that the Company will not for any such purpose be required
     to (1) qualify generally to do business as a foreign corporation in any
     jurisdiction where it would not otherwise be required to qualify but for
     the requirements of this subsection; (2) subject itself to taxation in any
     such jurisdiction; (3) consent to general service of process in any such
     jurisdiction; or (4) register or qualify Registrable Securities or take any
     other action under the state securities or "Blue Sky" laws of any
     jurisdiction if, in the reasonable good faith judgment of the Board of
     Directors of the Company, the consequences of the registration,
     qualification or other action would be unduly burdensome to the Company);

          (vi)   notify each seller of such Registrable Securities, at any time
     when a prospectus relating thereto is required to be delivered under the
     Securities Act, of the happening of any event which requires the making of
     any change in the prospectus included in such registration statement so
     that such document will not contain an untrue statement of a material fact
     or omit to state any material fact required to be stated therein or
     necessary to make the statements therein not misleading, and, at the
     request of any such seller, the Company will prepare a supplement or
     amendment to such prospectus so that such prospectus will not contain an
     untrue statement of a material fact or omit to state any material fact
     required to be stated therein or necessary to make the statements therein
     not misleading;

          (vii)  use its reasonable best efforts to cause all such Registrable
     Securities to be listed on each securities exchange or exchanges, automated
     quotation system or over-the-counter market upon which securities of the
     Company of the same class are then listed;

          (viii) enter into such customary agreements (including, without
     limitation, underwriting agreements in customary form, substance and scope)
     and take all such other action as the Holders of a majority of the
     Registrable Securities being sold or the underwriters, if any, reasonably
     request in order to expedite or facilitate the disposition of such
     Registrable Securities;

          (ix)   otherwise use its reasonable best efforts to comply with all
     applicable rules and regulations of the Commission;

          (x)    in the event of the issuance of any stop order suspending the
     effectiveness of a registration statement, or of any order suspending or
     preventing the use of any related prospectus or suspending the
     qualification of any securities included in such registration statement for
     sale in any jurisdiction, the Company will use its reasonable best efforts
     promptly to obtain the withdrawal of such order;

          (x)    use its reasonable best efforts to cause such Registrable
     Securities covered by such registration statement to be registered with or
     approved by such other foreign and domestic governmental agencies or
     authorities as may be necessary to enable the sellers thereof to consummate
     the disposition of such Registrable Securities;

          (xi)   use its reasonable best efforts to obtain a comfort letter from
     the Company's public accountants in customary form and covering such
     matters of the type customarily 

                                      -7-

 
     covered by comfort letters with respect to offerings of the type being made
     pursuant to the registration statement as the Holders of the Registrable
     Securities reasonably request; and

          (xii)  cooperate with each seller of such Registrable Securities to
     facilitate the timely preparation and delivery of certificates representing
     Registrable Securities to be sold and not bearing any restrictive legends.

     (b) Whenever the Holders of Registrable Securities have requested that any
Registrable Securities be registered pursuant to Section 2 or Section 3, each
Holder of Registrable Securities (including Registrable Securities in any
registration statement filed pursuant to this Agreement) will be deemed to have
agreed as follows:

          (i)    upon receipt of any notice from the Company of the happening of
     any event of the kind described in Section 4(a)(vi), the Holders of
     Registrable Securities covered by such registration statement will
     forthwith discontinue disposition of any such  Registrable Securities until
     the Holders of Registrable Securities receive copies of the supplemented or
     amended prospectus contemplated by Section 4(a)(vi), or until they are
     advised in writing by the Company that the use of the applicable prospectus
     may be resumed, and they have received copies of any additional or
     supplemental filings that are incorporated or deemed to be incorporated by
     reference in such prospectus (it being the agreement of the parties hereto,
     however, that the obligation of the Company with respect to maintaining the
     subject registration statement current and effective shall be extended by a
     period of days equal to the period the Holders of Registrable Securities
     are required by this Section 4(b)(i) to discontinue disposition of such
     Registrable Securities); and

          (ii)   furnish to the Company such information regarding each Holder,
     the Registrable Securities held by such Holder, the intended method of
     disposition thereof and such other information as the Company shall
     reasonably request and as shall be reasonably required in connection with
     the preparation of the applicable registration statement and other actions
     taken by the Company under this Agreement.

     (c) The Company may postpone the filing of any registration statement
required under Section 2 for a reasonable period of time, if (i) the Company has
been advised by legal counsel reasonably acceptable to the Holders of a majority
of the Registrable Securities that such filing would require the disclosure of a
material fact, and the Company determines reasonably and in good faith that such
disclosure would have a material adverse effect on the Company or (ii) (A) in
the good faith judgment of the Board of Directors of the Company, a required
registration under Section 2 would be seriously detrimental to the Company and
the Board of Directors of the Company concludes, as a result, that it is
essential to defer the filing of such registration statement at such time, and
(B) the Company shall furnish to the Holders of Registrable Securities a
certificate signed by the President of the Company stating that in the good
faith judgment of the Board of Directors of the Company, it would be seriously
detrimental to the Company for such registration statement to be filed in the
near future and that it is, therefore, essential to defer the filing of such
registration statement; provided, however, that under no circumstances shall one
or more delays pursuant to this Section 4(c) extend beyond the earlier to occur
of (x) the expiration of a period of ninety (90) days after receipt of the
request of a Holder of Registrable Securities and (y) that point in time at
which the 

                                      -8-

 
conditions described above no longer exist; and, provided further, that the
Company shall not defer its obligation pursuant to this Section 4(c) more than
once in any twelve-month period.

     SECTION 5.  EXPENSES OF REGISTRATION.  The Company shall pay all 
Registration Expenses in connection with each registration effected pursuant to
Sections 2 and 3 and, in any event, shall pay its internal expenses (including,
without limitation, all salaries and expenses of its officers and employees
performing legal and accounting duties), the expense of any annual audit and the
fees and expenses incurred in connection with the listing of the securities to
be registered on each securities exchange or market on which similar securities
issued by the Company are then listed.  All Selling Expenses incurred in
connection with a registration effected pursuant to the terms hereof shall be
borne by the seller or sellers of Registrable Securities.

     SECTION 6.  INDEMNIFICATION.

     (a) The Company shall indemnify and hold harmless, with respect to any
registration statement filed by it, to the fullest extent permitted by law, each
Holder of Registrable Securities covered by such registration statement, and
each other Person, if any, who controls such Holder within the meaning of
Section 15 of the Securities Act (collectively, "HOLDER INDEMNIFIED PARTIES")
against all losses, claims, damages, liabilities and expenses, joint or several
to which any such Holder Indemnified Party may become subject under the
Securities Act, the Exchange Act, at common law or otherwise, insofar as such
losses, claims, damages, liabilities or expenses (or actions or proceedings,
whether commenced or threatened, in respect thereof) arise out of or are based
upon (i) any untrue statement or alleged untrue statement of a material fact
contained in any registration statement in which such Registrable Securities
were included as contemplated hereby, or any post-effective amendment thereof,
or any omission or alleged omission to state therein a material fact required to
be stated therein or necessary to make the statements therein not misleading,
(ii) any untrue statement or alleged untrue statement of a material fact
contained in any preliminary, final or summary prospectus, together with the
documents incorporated by reference therein (as amended or supplemented if the
Company shall have filed with the Commission any amendment thereof or supplement
thereto), or any omission or alleged omission to state therein a material fact
required to be stated therein or necessary in order to make the statements
therein, in the light of the circumstances under which they were made, not
misleading, or (iii) any violation by the Company of any federal, state or
common law rule or regulation applicable to the Company and relating to action
of or inaction by the Company in connection with any such registration; and in
each such case, the Company shall reimburse each such Holder Indemnified Party
for any reasonable legal or other expenses incurred by any of them in connection
with investigating or defending any such loss, claim, damage, liability,
expense, action or proceeding; provided, however, that the Company shall not be
liable to any such Holder Indemnified Party in any such case to the extent that
any such loss, claim, damage, liability or expense (or action or proceeding,
whether commenced or threatened, in respect thereof) arises out 

                                      -9-

 
of or is based upon any untrue statement or alleged untrue statement or omission
or alleged omission made in such registration statement or amendment thereof or
supplement thereto or in any such preliminary, final or summary prospectus in
reliance upon and in conformity with written information furnished to the
Company by or on behalf of any such Holder Indemnified Party for use in the
preparation thereof; provided further that the Company shall not be liable to
any such Holder Indemnified Party in any such case to the extent that any such
loss, claim, damage, liability or expense (or action or proceeding, whether
commenced or threatened, in respect thereof) arises out of or is based upon any
untrue statement or alleged untrue statement or omission or alleged omission
made in any preliminary prospectus if (A) such holder failed to send or deliver
a copy of the prospectus with or prior to the delivery of written confirmation
of the sale of Registrable Securities and (B) the prospectus would have
completely corrected such untrue statement or omission; provided further that
the Company shall not be liable in any such case to the extent that any such
loss, claim, damage, liability or expense arises out of or is based upon an
untrue statement or alleged untrue statement or omission or alleged omission in
the prospectus, if such untrue statement or alleged untrue statement, omission
or alleged omission is completely corrected in an amendment or supplement to the
prospectus and if, having previously been furnished by or on behalf of the
Company with copies of the prospectus as so amended or supplemented, such holder
thereafter fails to deliver such prospectus as so amended or supplemented, prior
to or concurrently with the sale of a Registrable Security to the person
asserting such loss, claim, damage, liability or expense who purchased such
Registrable Security which is the subject thereof from such holder. Such
indemnity and reimbursement of expenses and other obligations shall remain in
full force and effect regardless of any investigation made by or on behalf of
the Holder Indemnified Parties and shall survive the transfer of such securities
by such Holder Indemnified Parties.

     (b) Each Holder of Registrable Securities participating in any registration
hereunder shall severally (and not jointly or jointly and severally) indemnify
and hold harmless, to the fullest extent permitted by law, the Company, its
directors, each of its officers who has signed the registration statement and
each Person who controls the Company (within the meaning of Section 15 of the
Securities Act) (collectively, "COMPANY INDEMNIFIED PARTIES") against all
losses, claims, damages, liabilities and expenses to which any Company
Indemnified Party may become subject under the Securities Act, the Exchange Act,
at common law or otherwise, and will reimburse each such Company Indemnified
Party for any reasonable legal or other expenses incurred by any of them in
connection with investigating or defending any such loss, claim, damage,
liability, expense, action or proceeding, but only insofar as such losses,
claims, damages, liabilities or expenses (or actions or proceedings, whether
commenced or threatened, in respect thereof) arise out of or are based upon (i)
any untrue statement or alleged untrue statement of a material fact contained in
any registration statement in which such Holder's Registrable Securities were
included or the omission or alleged omission to state therein a material fact
required to be stated therein or necessary to make the statements therein not
misleading,  (ii) any untrue statement or alleged untrue statement of a material
fact contained in any preliminary, final or summary prospectus, together with
the documents incorporated by reference therein (as amended or supplemented if
the Company shall have filed with the Commission any amendment thereof or
supplement thereto), or the omission or alleged omission to state therein a
material fact required to be stated therein or necessary in order to make the
statements therein, in the light of the circumstances under which they were
made, not misleading, in each case to the extent (and only to the extent) that
such untrue statement or omission or alleged untrue statement or omission was
made in reliance upon and in conformity with information furnished in writing by
or on behalf of such Holder specifically for use in connection with such
registration, (iii) any violation by the Holder of any federal, state or common
law, rule or regulation applicable to the Holder and relating to action of or
inaction by the Holder in connection with any registration statement and (iv)
with respect to any preliminary prospectus, the fact that the Holder sold
Registrable Securities to a person to whom there was not sent or given, at or
prior to the written confirmation of the sale, a copy of the prospectus
(excluding documents incorporated by 

                                     -10-

 
reference) or of the prospectus as then amended or supplemented (excluding
documents incorporated by reference) if (a) the Company has previously furnished
copies thereof to the Holder in compliance with Section 4 and (b) the loss,
claim, damage, liability or expense of the Company Indemnified Party results
from an untrue statement or omission of a material fact contained in the
preliminary prospectus which was corrected in the prospectus (or the prospectus
as amended or supplemented). Such indemnity obligation shall remain in full
force and effect regardless of any investigation made by or on behalf of the
Company Indemnified Parties (except as provided above) and shall survive the
transfer of such securities by such Holder.

     (c) Promptly after receipt by an indemnified party under subsection (a) or
(b) of written notice of the commencement of any action, suit, proceeding,
investigation or threat thereof made in writing with respect to which a claim
for indemnification may be made pursuant to this Section 6, such indemnified
party shall, if a claim in respect thereof is to be made against an indemnifying
party, give prompt written notice to the indemnifying party of the threat or
commencement thereof; provided, however, that the failure to so promptly notify
the indemnifying party shall not relieve it from any liability which it may have
to any indemnified party except to the extent that the indemnifying party is
actually prejudiced by such failure to give prompt notice.  If any such claim or
action referred to under subsection (a) or (b) is brought against any
indemnified party and it then notifies the indemnifying party of the threat or
commencement thereof, the indemnifying party shall be entitled to participate
therein and, to the extent that it wishes, jointly with any other indemnifying
party similarly notified, to assume the defense thereof with counsel reasonably
satisfactory to such indemnified party.  After notice from the indemnifying
party to such indemnified party of its election so to assume the defense of any
such claim or action, the indemnifying party shall not be liable to such
indemnified party under this Section 6 for any legal expenses of counsel or any
other expenses subsequently incurred by such indemnified party in connection
with the defense thereof other than reasonable costs of investigation unless the
indemnifying party has failed to assume the defense of such claim or action or
to employ counsel reasonably satisfactory to such indemnified party.  Under no
circumstances will the indemnifying party be obligated to pay the fees and
expenses of more than one law firm for all indemnified parties.  The
indemnifying party shall not be required to indemnify the indemnified party with
respect to any amounts paid in settlement of any action, proceeding or
investigation entered into without the written consent of the indemnifying
party, which consent shall not be unreasonably withheld.  No indemnifying party
shall consent to the entry of any judgment or enter into any settlement without
the consent of the indemnified party unless (i) such judgment or settlement does
not impose any obligation or liability upon the indemnified party other than the
execution, delivery or approval thereof, and (ii) such judgment or settlement
includes as an unconditional term thereof the giving by the claimant or
plaintiff to such indemnified party of a full release and discharge from all
liability in respect of such claim.

     (d) Indemnification similar to that specified in the preceding subsections
of this Section 6 (with appropriate modifications) shall be given by the Company
and each seller of Registrable Securities with respect to any required
registration or qualification of securities under any state securities or blue
sky laws.

     (e) If the indemnification provided for in this Section 6 is unavailable to
or insufficient to hold harmless an indemnified party under subsection (a) or
(b), then each indemnifying party shall contribute to the amount paid or payable
by such indemnified party as a result of the losses, claims, damages,
liabilities or expenses (or actions or proceedings in respect thereof) referred
to in subsection 

                                     -11-

 
(a) or (b) in such proportion as is appropriate to reflect the relative fault of
the indemnifying party on the one hand and the indemnified party on the other in
connection with the statements, omissions, actions or inactions which resulted
in such losses, claims, damages, liabilities or expenses as well as any other
relevant equitable considerations. The relative fault of the indemnifying party
and the indemnified party shall be determined by reference to, among other
things, whether the untrue or alleged untrue statement of a material fact or the
omission or alleged omission to state a material fact relates to information
supplied by the indemnifying party or the indemnified party, any action or
inaction by any such party, and the parties' relative intent, knowledge, access
to information and opportunity to correct or prevent such statement, omission,
action or inaction. The amount paid or payable by an indemnified party as a
result of the losses, claims, damages, liabilities or expenses (or actions or
proceedings in respect thereof) pursuant to this subsection (e) shall be deemed
to include, without limitation, any reasonable legal or other expenses incurred
by such indemnified party in connection with investigating or defending any such
action or claim (which shall be limited as provided in subsection (c) if the
indemnifying party has assumed the defense of any such action in accordance with
the provisions thereof) which is the subject of this subsection (e). No person
guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of
the Securities Act) shall be entitled to contribution from any person who was
not guilty of such fraudulent misrepresentation. Promptly after receipt by an
indemnified party under this subsection (e) of written notice of the
commencement of any action, suit, proceeding, investigation or threat thereof
made in writing with respect to which a claim for contribution may be made
against an indemnifying party under this subsection (e), such indemnified party
shall, if a claim for contribution in respect thereof is to be made against an
indemnifying party, give prompt written notice to the indemnifying party in
writing of the commencement thereof (if the notice specified in subsection (c)
has not been given with respect to such action); provided, however, that the
failure to so promptly notify the indemnifying party shall not relieve it from
any obligation to provide contribution which it may have to any indemnified
party under this subsection (e) except to the extent that the indemnifying party
is actually prejudiced by the failure to give prompt notice.

     The parties hereto agree that it would not be just and equitable if
contribution pursuant to this paragraph were determined by pro rata allocation
or by any other method of allocation which does not take account the equitable
considerations referred to in the immediately preceding paragraph.

     If indemnification is available under this Section 6, the indemnifying
parties shall indemnify each indemnified party to the fullest extent provided in
subsections (a) and (b), without regard to the relative fault of said
indemnifying party or any other equitable consideration provided for in this
subsection.  The provisions of this subsection shall be in addition to any other
rights to indemnification or contribution which any indemnified party may have
pursuant to law or contract, shall remain in full force and effect regardless of
any investigation made by or on behalf of any indemnified party, and shall
survive the transfer of securities by any such party.

     (f) In connection with any underwritten offering contemplated by this
Agreement which includes Registrable Securities, the Company and all sellers of
Registrable Securities included in any registration statement shall agree to
customary provisions for indemnification and contribution (consistent with the
other provisions of this Section 6) in respect of losses, claims, damages,
liabilities and expenses of the underwriters of such offering.

                                     -12-

 
     SECTION 7.  SELECTION OF UNDERWRITERS.  If a registration effected
pursuant to Section 2 is an underwritten offering or a best efforts underwritten
offering, the investment bankers or investment bankers and manager or managers
that will administer the offering shall be selected by the Holders of a majority
of the Registrable Securities to be registered in such registration; provided,
however, that such investment bankers and managers must be reasonably
satisfactory to the Company.

     SECTION 8.  RULE 144.  The Company covenants to each Holder that, to the
extent that the Company shall be required to do so under the Exchange Act, the
Company shall (a) timely file the reports required to be filed by it under the
Exchange Act or the Securities Act (including, but not limited to, the reports
under Section 13 and 15(d) of the Exchange Act referred to in subparagraph (c)
(1) of Rule 144 adopted by the Commission under the Securities Act) and the
rules and regulations adopted by the Commission thereunder, and (b) take such
further action as any Holder may reasonably request, all to the extent required
from time to time to enable such Holder to sell Registrable Securities without
registration under the Securities Act within the limitations of the exemption
provided by Rule 144 under the Securities Act, as such Rule may be amended from
time to time, or any similar rule or regulation hereafter adopted by the
Commission.  Upon the reasonable request of any Holder, the Company shall
deliver to such Holder a written statement as to whether it has complied with
such requirements.

     Section 9.  Participation in Underwritten Registrations.  In the case of
a registration hereunder, if the Company has determined to enter into an
underwriting agreement in connection therewith, all shares of Registrable
Securities to be included in such registration shall be subject to the
underwriting agreement, which shall be in customary form and contain such terms
as are customarily contained in such agreements, and the Holders may not
participate in any such registration unless the Holder (a) agrees to sell its
securities on the basis provided in any underwriting arrangements and (b)
completes and executes all questionnaires, power of attorney, indemnities,
underwriting agreements and other documents reasonably required under the terms
of the underwriting arrangements.

     Section 10. Rights to Withdraw From Registration.  If, as a result of
the proration provisions of Section 3(b) a Holder is not entitled to include all
Registrable Securities in a registration that the Holder has requested to be
included, the Holder may elect to withdraw its request to include Registrable
Securities in the registration (a "Withdrawal Election"); provided, however,
that a Withdrawal Election shall be irrevocable and, after making a Withdrawal
Election, the Holder shall no longer have any right to include Registrable
Securities in the registration as to which the Withdrawal Election was made.

     SECTION 11. EXISTING REGISTRATION RIGHTS.  The Company and each of the
Initial Shareholders represent and warrant to, and covenant with, the New
Shareholders as follows:

     (a) As of the date hereof, the Company has not entered into any agreement,
written or oral, granting or otherwise affording to a third party registration
rights with respect to any securities held by such third party in the Company,
except for the Difco Agreement and the LaSalle Agreement.

     SECTION 12. MISCELLANEOUS.

                                     -13-

 
     (a) From and after the date of this Agreement, the Company will not enter
into any agreement with respect to its securities which is inconsistent with or
violates the rights granted to the Holders of Registrable Securities in this
Agreement.

     (b) Each Holder of Registrable Securities (including Registrable Securities
in any registration statement filed pursuant to this Agreement) agrees as
follows:

          (i)  if any Registrable Securities are being registered in any
     registration pursuant to this Agreement, the Holder thereof will comply
     with all anti-stabilization, manipulation and similar provisions of Section
     10 of the Exchange Act, as amended, and any rules promulgated thereunder by
     the Commission and, at the request of the Company, will execute and deliver
     to the Company and to any underwriter participating in such offering, an
     appropriate agreement to such effect; and

          (ii) at the end of any period during which the Company is obligated to
     keep a registration statement current and effective as described herein,
     the Holders of Registrable Securities included in the registration
     statement shall discontinue sales thereof pursuant to such registration
     statement.

     (c) In order to facilitate the possibility of future public offerings of
Ordinary Shares, the Holders (and any subsequent Holder) agree that the
Registrable Securities will not be resold during a period commencing on the
filing by the Company of a registration statement under the Securities Act for
an underwritten  public offering for cash by the Company of its Ordinary Shares
or securities convertible into or exercisable or exchangeable for its Ordinary
Shares and continuing until the earlier of the abandonment of the proposed
public offering or 120 days following the date of the last closing in the public
offering without the consent of the underwriters of such offering, except to the
extent such shares are included in such registration. Holders of such
Registrable Securities also agree that they will cooperate with the Company in
providing reasonable written assurances respecting the foregoing to the
underwriter of any such public offering.  Holders agree that during the above
restricted period they will not directly or indirectly sell, offer to sell,
contract to sell (including without limitation any short sale), grant an option
to purchase or otherwise transfer or dispose of (other than to donees who agree
to be similarly bound) shares of Registrable Securities at any time during such
period except securities included in such registration.  In order to enforce the
foregoing covenant, the Company may impose stop-order instructions with respect
to such shares of Registrable Securities held by each Holder, which shall be
binding upon any assignee or successor of such Holder (and the shares or
securities of every other person subject to the foregoing restriction), until
the end of the restricted period.

     (d) All questions concerning the construction, validity and interpretation
of this Agreement shall be governed by the internal law, and not the law of
conflicts, of the State of Texas.

     (e) All covenants and agreements in this Agreement by or on behalf of any
of the parties hereto will bind and inure to the benefit of the respective
successors and assigns of the parties hereto. In addition, the rights and
obligations under this Agreement shall  automatically be transferred to and
binding on any transferee or assignee of the Registrable Securities; provided,
that (i) the Company is, within a reasonable time after such transfer, furnished
with written notice of the name and address 

                                     -14-

 
of such transferee or assignee and the Registrable Securities with respect to
which such registration rights are being transferred or assigned, (ii) such
transferee or assignee agrees in writing to be bound by and subject to the terms
and conditions of this Agreement, (iii) the transfer and assignment of the
subject Registrable Securities is in compliance with (A) the Purchase Agreement
and (B) the Securities Act and applicable state securities laws or an exemption
from the registration requirements of the Securities Act and applicable state
securities laws, (iv) such assignment of rights and obligations under this
Agreement shall be effective only if immediately following such transfer the
further disposition of such Registrable Securities by the transferee or assignee
is restricted under the Securities Act and (v) the transferee acquires at least
10% of the Registrable Securities originally purchased by the New Shareholders
from the Company.

     (f) This Agreement is intended by the parties as a final expression of
their agreement and intended to be a complete and exclusive statement of the
agreement and understanding of the parties hereto in respect of the subject
matter herein contained.  There are no restrictions, promises, warranties or
undertakings, other than those set forth or referred to herein, with respect to
the registration rights granted by the Company to the Holders of the Registrable
Securities.  This Agreement supersedes all prior agreements and understandings
between the parties with respect to such subject matter.

     (g) All notices, demands or other communications to be given or delivered
under or by reason of the provisions of this Agreement shall be in writing and
shall be deemed to have been given when delivered personally or sent by
reputable express courier service (charges prepaid), or mailed to the recipient
by certified or registered mail, return receipt requested and postage prepaid,
or sent by telefax, to the parties at the following address (or to such other
address or to the attention of such other person as the recipient party has
specified by prior like notice to the sending party):

                                     -15-

 
     If to the Company:
 
               Alliance Resources PLC
               4200 East Skelly Drive, Suite 1000
               Tulsa, Oklahoma  74135
               Attention:  John A. Keenan
               Fax No.: 918-494-4918
 
     If to either EnCap LP
     or ECIC:

               Energy Capital Investment Company PLC
               EnCap Equity 1996 Limited Partnership
               c/o EnCap Investments L.C.
               1100 Louisiana, Suite 3150
               Houston, Texas  77002
               Attention: Robert L. Zorich
               Fax No.: 713-659-6130

     If to EnCap LC:

               EnCap Investments L.C.
               1100 Louisiana, Suite 3150
               Houston, Texas  77002
               Attention: Robert L. Zorich
               Fax No.: 713-659-6130

     (h) If any provision of this Agreement is held to be unenforceable, this
Agreement shall be considered divisible and such provision shall be deemed
inoperative to the extent it is deemed unenforceable, and in all other respects
this Agreement shall remain in full force and effect; provided, however, that if
any such provision may be made enforceable by limitation thereof, then such
provision shall be deemed to be so limited and shall be enforceable to the
maximum extent permitted by applicable law.

     (i) This Agreement may be executed by the parties hereto in any number of
counterparts, each of which shall be deemed an original, but all of which shall
constitute one and the same agreement.  Each counterpart may consist of a number
of copies hereof each signed by less than all, but together signed by all, the
parties hereto.

     (j) Each Holder of Registrable Securities, in addition to being entitled to
exercise all rights granted by law, including recovery of damages, will be
entitled to specific performance of its rights under this Agreement.  Each party
agrees that monetary damages would not be adequate compensation for any loss
incurred by reason of breach by it of the provisions of this Agreement and
hereby agrees to waive (to the extent permitted by law) the defense in any
action for specific performance that a remedy of law would be adequate.

                                     -16-

 
     (k) In any action or proceeding brought to enforce any provision of this
Agreement, or where any provision hereof is validly asserted as a defense, the
successful party shall be entitled to recover reasonable attorneys' fees in
addition to any other available remedy.

     (l) The Company agrees to remove any legends on certificates representing
Registrable Securities describing transfer restrictions applicable to such
securities upon the sale of such securities (i) pursuant to an effective
Registration Statement under the Securities Act or (ii) in accordance with the
provisions of Rule 144 under the Securities Act.



                    [REMAINDER OF PAGE INTENTIONALLY BLANK]

                                     -17-

 
  IN WITNESS WHEREOF, the parties have caused this Agreement to be duly executed
                      as of the date first above written.

                             ENCAP EQUITY 1996 LIMITED PARTNERSHIP

                             By:  ENCAP INVESTMENTS L.C., General Partner


                             By:
                                ------------------------------------------------
                                Name:  Robert L. Zorich
                                Title: Managing Director


                             ENERGY CAPITAL INVESTMENT COMPANY PLC


                             By:
                                ------------------------------------------------
                                Name:  Gary R. Petersen
                                Title: Director


                             ENCAP INVESTMENTS L.C.


                             By:
                                ------------------------------------------------
                                Name:  Robert L. Zorich
                                Title: Managing Director


                             ALLIANCE RESOURCES PLC


                             By:
                                ------------------------------------------------
                                Name:
                                     -------------------------------------------
                                Title:
                                      ------------------------------------------

                                     -18-