<PAGE>
                                                                    EXHIBIT 10.2

                             LETTER AMENDMENT NO. 1



                                                Dated as of December 7, 2001

To the banks, financial institutions
and other institutional lenders
(collectively, the "Lenders") parties
to the Credit Agreement referred to
below and to JPMorgan Chase Bank
(formerly The Chase Manhattan Bank),
as Paying Agent, and JPMorgan Chase Bank
and Citicorp USA, Inc., as Co-Administrative Agents
for the Lenders

Ladies and Gentlemen:

         We refer to the Credit Agreement dated as of August 16, 1999 (as
amended, supplemented or otherwise modified through the date hereof, the "Credit
Agreement") among the undersigned and you. Capitalized terms not otherwise
defined in this Letter Amendment have the same meanings as specified in the
Credit Agreement.

         We are currently negotiating a transaction to acquire the Beacon
Investors' controlling interest in Alliance Resource Management GP, LLC, the
managing general partner entity created to manage the partnership assets of the
Borrower, and have requested that the Lenders agree to amend the definition of
"Change of Control" set forth in Article I of the Credit Agreement and to make
such other amendments as may be necessary to permit the transfer of the
controlling interest to management.


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         In addition Toptiki Coal, LLC ("Toptiki"), a former direct subsidiary
of the Borrower, was a small surface and underground mining company whose mining
operations were discontinued due to uneconomic conditions. The Borrower has
continued to fund annual holding costs since closure including lease royalty
payments and reclamation bonding expenses. In November 2000, the Borrower sold
its member interest in Toptiki to Middlefork Land Company, Inc. for $25,000 plus
the assumption of outstanding Toptiki liabilities.

         Pursuant to the Credit Agreement, Toptiki had entered into a Subsidiary
Guaranty in favor of the Lenders. As part of the divestiture transaction, the
Borrower indemnified the Toptiki buyer from any associated claims under said
guaranty. With the sale of Toptiki, the Borrower requests the Lenders terminate
and release the Subsidiary Guaranty issued by Toptiki.

         You have indicated your willingness, on the terms and conditions stated
below, to so agree. Accordingly, it is hereby agreed by you and us as follows:

                  SECTION 1. The Credit Agreement is, effective as of the date
         of this Letter Amendment, hereby amended as follows:

a. The definition of "Change of Control" set forth in Section 1.01 shall be
amended in full to read as follows:

                          "'CHANGE OF CONTROL' means the occurrence of either of
                                    the following: (a) Management Investors,
                                    Beacon Investors and/or the Beacon
                                    Controlled Affiliates shall at any time for
                                    any reason cease collectively to own,
                                    directly or indirectly, at least 51% of the
                                    managing ownership interest of the sole or
                                    managing general partner, as the case may
                                    be, of the Borrower or (b) the managing
                                    general partner of the Borrower shall at any
                                    time for any reason cease to be the sole or
                                    managing general partner of Alliance
                                    Resources Partners, L.P."

b. Section 1.01 is amended by adding the following definition in the appropriate
alphabetical order:

                          "'MANAGEMENT INVESTORS' means, collectively, certain
                                    Persons contemplated to be formed by the
                                    management, officers and/or directors of the
                                    Borrower and named Alliance Management
                                    Holdings, LLC, any of ARH II, LLC and/or
                                    Alliance Resource Holdings II, LLC,
                                    including the management, officers and/or
                                    directors who are shareholders and/or
                                    members of any of such Persons."


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                  SECTION 2. The Lenders, by their signature below, hereby
         consent to the release of Toptiki Coal, LLC, as a Subsidiary Guarantor.

         This Letter Amendment (other than Section 1 hereof) shall become
effective as of the date first above written when, and only when, the Paying
Agent shall have received counterparts of this Letter Amendment executed by the
undersigned and all of the Lenders or, as to any of the Lenders, advice
satisfactory to the Paying Agent that such Lender has executed this Letter
Amendment. Section 1 of this Letter Amendment shall become effective as of the
date first above written when, and only when, the Paying Agent shall have
received counterparts of this Letter Amendment executed by the undersigned and
the Required Lenders or, as to any of the Lenders, advice satisfactory to the
Paying Agent that such Lender has executed this Letter Amendment. The
effectiveness of this Letter Amendment is conditioned upon the accuracy of the
factual matters described herein. This Letter Amendment is subject to the
provisions of Section 8.01 of the Credit Agreement.

         On and after the effectiveness of this Letter Amendment, each reference
in the Credit Agreement to "this Agreement", "hereunder", "hereof" or words of
like import referring to the Credit Agreement, and each reference in the Notes
and each of the other Loan Documents to "the Credit Agreement", "thereunder",
"thereof" or words of like import referring to the Credit Agreement, shall mean
and be a reference to the Credit Agreement, as amended by this Letter Amendment.

         The Credit Agreement, the Notes and each of the other Loan Documents,
as specifically amended by this Letter Amendment, are and shall continue to be
in full force and effect and are hereby in all respects ratified and confirmed.
The execution, delivery and effectiveness of this Letter Amendment shall not,
except as expressly provided herein, operate as a waiver of any right, power or
remedy of any Lender or any Agent under any of the Loan Documents, nor
constitute a waiver of any provision of any of the Loan Documents.

         If you agree to the terms and provisions hereof, please evidence such
agreement by executing and returning at least one signature page of this Letter
Amendment by fax to Shearman & Sterling, fax no. +44 207 655 5500 Attn. Jolene
Harvey by 5:00p.m. (London time) on Wednesday, December 19, 2001 with an
original executed signature page to JPMorgan Chase Bank, 270 Park Avenue, 23rd
Floor, New York, NY 10017, Attn. Peter S. Predun for delivery by 5:00p.m. (New
York time) on Friday, December 21, 2001.

         This Letter Amendment may be executed in any number of counterparts and
by different parties hereto in separate counterparts, each of which when so
executed shall be deemed to be an original and all of which taken together shall
constitute one and the same agreement. Delivery of


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an executed counterpart of a signature page to this Letter Amendment by
telecopier shall be effective as delivery of an original executed counterpart of
this Letter Amendment.


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         This Letter Amendment shall be governed by, and construed in accordance
with, the laws of the State of New York.

                                      Very truly yours,


                                      ALLIANCE RESOURCE OPERATING PARTNERS, L.P.


                                      By: ALLIANCE RESOURCE MANAGEMENT GP, LLC,
                                             its Managing General Partner


                                      By   /s/ Michael L. Greenwood
                                           -------------------------------------
                                           Name:  Michael L. Greenwood
                                           Title: Senior Vice President & Chief
                                                    Financial Officer





<PAGE>


Agreed as to the foregoing Letter Amendment (other than Section 1 thereof) as of
the date first above written:

JPMORGAN CHASE BANK,
   as Paying Agent, Co-Administrative Agent and Lender

By   /s/ Peter S. Predun
     ----------------------------
     Name: Peter S. Predun
     Title: Vice President





Agreed as to Section 1 of the foregoing Letter Amendment as of the date first
above written:


JPMORGAN CHASE BANK,
   as Paying Agent, Co-Administrative Agent and Lender

By   /s/ Peter S. Predun
     ----------------------------
     Name: Peter S. Predun
     Title: Vice President







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                             Agreed as to the foregoing Letter Amendment
                             (other than Section 1 thereof) as of the date first
                             above written:


CITICORP USA, INC.,
   as Co-Administrative Agent and Lender


By   /s/ Larry Farley
     ----------------------------
     Name: Larry Farley
     Title: Director



Agreed as to Section 1 of the foregoing Letter Amendment as of the date first
above written:

CITICORP USA, INC.,
   as Co-Administrative Agent and Lender


By   /s/ Larry Farley
     ----------------------------
     Name: Larry Farley
     Title: Director



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Agreed as to the foregoing Letter Amendment (other than Section 1 thereof) as of
the date first above written:

The Fuji Bank Ltd.
------------------------------
[NAME OF LENDER]


By   /s/ Yuji Tanaka
     -------------------------
     Name: Yuji Tanaka
     Title: V.P. & Manager


Agreed as to Section 1 of the foregoing Letter Amendment as of the date first
above written:


The Fuji Bank Ltd.
------------------------------
[NAME OF LENDER]


By   /s/ Yuji Tanaka
     -------------------------
     Name: Yuji Tanaka
     Title: V.P. & Manager


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Agreed as to the foregoing Letter Amendment (other than Section 1 thereof) as of
the date first above written:

Bank of Montreal
------------------------------
[NAME OF LENDER]


By   /s/ Ian M. Plester
     -------------------------
     Name: Ian M. Plester
     Title: V.P. & Manager


Agreed as to Section 1 of the foregoing Letter Amendment as of the date first
above written:


Bank of Montreal
------------------------------
[NAME OF LENDER]


By   /s/ Ian M. Plester
     -------------------------
     Name: Ian M. Plester
     Title: V.P. & Manager


<PAGE>

Agreed as to the foregoing Letter Amendment (other than Section 1 thereof) as of
the date first above written:

Fleet National Bank
------------------------------


By   /s/ Jeffrey RathKamp
     -------------------------
     Name: Jeffrey RathKamp
     Title: Vice President


Agreed as to Section 1 of the foregoing Letter Amendment as of the date first
above written:


Fleet National Bank
------------------------------


By   /s/ Jeffrey RathKamp
     -------------------------
     Name: Jeffrey RathKamp
     Title: Vice President


<PAGE>

Agreed as to the foregoing Letter Amendment (other than Section 1 thereof) as of
the date first above written:

The Industrial Bank of Japan, Limited
-------------------------------------
[NAME OF LENDER]


By   /s/ John Dippo
     --------------------------------
     Name: John Dippo
     Title: Senior Vice President

<PAGE>

Agreed as to the foregoing Letter Amendment (other than Section 1 thereof) as of
the date first above written:

Bank Trust Company
------------------------------
[NAME OF LENDER]


By   /s/ Marcus M. Tarkington
     -------------------------
     Name: Marcus M. Tarkington
     Title: Director


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Agreed as to the foregoing Letter Amendment (other than Section 1 thereof) as of
the date first above written:

Bank of Oklahoma, N.A.
---------------------------------
[NAME OF LENDER]


By   /s/ Robert D. Mattax
     ----------------------------
     Name: Robert D. Mattax
     Title: Senior Vice President


Agreed as to Section 1 of the foregoing Letter Amendment as of the date first
above written:


Bank of Oklahoma, N.A.
---------------------------------
[NAME OF LENDER]


By   /s/ Robert D. Mattax
     ----------------------------
     Name: Robert D. Mattax
     Title: Senior Vice President


<PAGE>


                                     CONSENT



                                                    Dated as of December 7, 2001

         Each of the undersigned, as Guarantors under the Subsidiary Guaranty
dated August 16, 1999 (the "Guaranty") in favor of the Lender Parties and the
Agents, each as defined in the Credit Agreement referred to in the foregoing
Letter Amendment, hereby consents to such Letter Amendment and hereby confirms
and agrees that (a) notwithstanding the effectiveness of such Letter Amendment,
the Guaranty is, and shall continue to be, in full force and effect and is
hereby ratified and confirmed in all respects, except that, on and after the
effectiveness of such Letter Amendment, each reference in the Guaranty to the
"Credit Agreement", "thereunder", "thereof" or words of like import shall mean
and be a reference to the Credit Agreement, as amended by such Letter Amendment,
and (b) each Guarantor does, and shall continue to, absolutely, unconditionally
and irrevocably guarantee the punctual payment when due of all Guaranteed
Obligations (as defined in the Guaranty).

                                    ALLIANCE COAL, LLC

                                    By:    Alliance Resource GP, LLC

                                           By: /s/ Michael L. Greenwood
                                               ---------------------------------
                                               Name: Michael L. Greenwood
                                               Title: SVP & CFO

                                    ALLIANCE LAND, LLC
                                    ALLIANCE PROPERTIES, LLC
                                    BACKBONE MOUNTAIN, LLC
                                    EXCEL MINING, LLC
                                    GIBSON COUNTY COAL, LLC
                                    HOPKINS COUNTY COAL, LLC
                                    MCMINING, LLC
                                    METTIKI COAL, LLC
                                    METTIKI COAL (WV), LLC
                                    MT. VERNON TRANSFER TERMINAL, LLC
                                    PONTIKI COAL, LLC
                                    WEBSTER COUNTY COAL, LLC
                                    WHITE COUNTY COAL, LLC

                                    By:    Alliance Coal, LLC

                                           By:   Alliance Resource GP, LLC

                                                 By: /s/ Michael L. Greenwood
                                                     ---------------------------
                                                     Name: Michael L. Greenwood
                                                     Title: SVP & CFO