Exhibit 10.4

AMENDMENT TO

OMNIBUS AGREEMENT

This Amendment (the “Amendment”) to the Omnibus Agreement is made and entered
into as of May 8, 2002, by and among Alliance Resource Partners, L.P., a
Delaware limited partnership (the “MLP”), Alliance Resource Holdings, Inc., a
Delaware corporation (“ARH”), Alliance Resource GP, LLC, a Delaware limited
liability company and special general partner of the MLP (the “SGP”) and
Alliance Resource Management GP, LLC, a Delaware limited liability company and
managing general partner of the MLP (the “MGP”).

RECITALS

WHEREAS, the MLP, ARH, the SGP and the MGP entered into the Omnibus Agreement,
dated as of August 20, 1999 (the “Agreement”); and

WHEREAS, pursuant to the terms of that certain Purchase Agreement (the “Purchase
Agreement”) of even date herewith by and among Beacon-Alliance Limited Member,
LLC (“BALM”), Beacon-Alliance Managing Member, LLC (“BAMM”), and Alliance
Management Holdings-II (“AMH-II”). BALM is selling to AMH-II its 74.09% limited
liability company interest in the MGP, and BAMM is selling to AMH-II its 0.01%
limited liability company interest in the MGP; and

WHEREAS, immediately prior to the execution of this Amendment, (i) certain
employee stockholders in ARH are exchanging their shares of common stock in ARH
to Alliance Resource Holdings II, Inc. (“ARH-II”) in exchange for shares of
common stock in ARH-II, and (ii) ARH-II is purchasing the shares of common stock
in ARH owned by The Beacon Group Energy Investment Fund, L.P., MPC Partners, LP,
John P. Neafsey, Michael L. Greenwood, and S. Paul Mackey in each case pursuant
to the terms and conditions of that certain Exchange Agreement of even date
herewith (the “Exchange Agreement”); and

WHEREAS, concurrently with the consummation of the transactions contemplated by
the Purchase Agreement and the Exchange Agreement, the MLP, ARH, the SGP and the
MGP desire to amend the Agreement as set forth herein;

NOW, THEREFORE, in consideration of the mutual promises and covenants made
herein, and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties agree as follows:

Section 1. Amendments to Agreement.

The Agreement is hereby amended as follows:

(a) AMH-II, LLC and ARH-II shall be joined as parties to this Agreement and
shall be bound by all of its terms.

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(b) Section 2.4 of the Agreement is hereby deleted in its entirety and replaced
with the following:

2.4 Termination. The provisions of this Article II may be terminated by ARH upon
or at any time after a “Change of Control” of ARH or the MGP by written notice
to the MLP. A Change of Control of ARH or the MGP shall be deemed to have
occurred upon the occurrence of one or more of the following events: (i) any
sale, lease, exchange or other transfer (in one transaction or a series of
related transactions) of all or substantially all of the assets of ARH or the
MGP to any Person or its Affiliates, unless immediately following such sale,
lease, exchange or other transfer such assets are owned, directly or indirectly,
by the ARH Entities or the MGP; (ii) the consolidation or merger of ARH or the
MGP with or into another Person pursuant to a transaction in which the
outstanding Voting Stock of ARH or the MGP is changed into or exchanged for
cash, securities or other property, other than any such transaction where
(a) the outstanding Voting Stock of ARH or the MGP is changed into or exchanged
for Voting Stock of the surviving corporation or its parent and (b) the holders
of the Voting Stock of ARH or the MGP immediately prior to such transaction own,
directly or indirectly, not less than a majority of the Voting Stock of the
surviving corporation or its parent immediately after such transaction; or
(iii) a “person” or “group” (within the meaning of Sections 13(d) or 14(d)(2) of
the Exchange Act) being or becoming the “beneficial owner” (as defined in Rules
13d-3 and 13d-5 under the Exchange Act) of more than 50% of all Voting Stock of
ARH or the MGP then outstanding, other than in a merger or consolidation which
would not constitute a Change of Control under clause (ii) above. None of the
transactions contemplated by the Purchase Agreement and the Exchange Agreement
shall constitute a Change of Control.

(c) The definition of “AHR Entities” in Article I is hereby deleted in its
entirety and replaced with the following:

“ARH Entities” shall mean ARH and any of its Affiliates, including ARH-II.

“Purchase Agreement” shall mean that certain Purchase Agreement dated as of the
date hereof by and among Beacon-Alliance Limited Member, LLC (“BALM”),
Beacon-Alliance Managing Member, LLC (“BAMM”), and Alliance Management
Holdings-II (“AMH-II”). BALM is selling to AMH-II its 74.09% limited liability
company interest in the MGP, and BAMM is selling to AMH-II its 0.01% limited
liability company interest in the MGP.

“Exchange Agreement” shall mean that certain Exchange Agreement dated as of the
date hereof by which (i) certain employee stockholders in ARH are exchanging
their shares of common stock in ARH to Alliance Resource Holdings II, Inc.
(“ARH-II”) in exchange for shares of common stock in ARH-II, and (ii) ARH-II is
purchasing the shares of common stock in ARH owned by The Beacon Group Energy
Investment Fund, L.P., MPC Partners, LP, John P. Neafsey, Michael L. Greenwood,
and S. Paul Mackey.

Section 2. Definitions.

All capitalized terms used in this Amendment without definition have the
meanings given to them in the Agreement.

 

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Section 3. Governing Law.

This Amendment shall be construed and enforced in accordance with the laws of
the state of Delaware without regard to the conflicts of law principles thereof.

Section 4. Force and Effect of Unmodified Provisions of the Agreement.

Except as expressly modified by this Amendment, the terms of the Agreement shall
remain unchanged and the Agreement shall continue in full force and effect. The
Agreement and this Amendment shall be considered one and the same agreement.

Section 5. Counterparts.

This Amendment may be signed in any number of counterparts with the same effect
as if the signatures on each such counterparts were on the same instrument.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be executed
as of the date and year first above written.

 

ALLIANCE RESOURCE HOLDINGS, INC.

By:

 

/s/ Thomas L. Pearson

 

Name:

 

Thomas L. Pearson

 

Title:

 

Senior Vice President - Law and

Administration, General Counsel and Secretary

 

ALLIANCE RESOURCE PARTNERS, L.P.

By:

 

/s/ Thomas L. Pearson

 

Name:

 

Thomas L. Pearson

 

Title:

 

Senior Vice President - Law and

Administration, General Counsel and Secretary

 

ALLIANCE RESOURCE MANAGEMENT GP, LLC

By:

 

/s/ Thomas L. Pearson

 

Name:

 

Thomas L. Pearson

 

Title:

 

Senior Vice President - Law and

Administration, General Counsel and Secretary

 

ALLIANCE RESOURCE GP, LLC

By:

 

/s/ Thomas L. Pearson

 

Name:

 

Thomas L. Pearson

 

Title:

 

Senior Vice President - Law and

Administration, General Counsel and Secretary

Amendment to Omnibus Agreement

Signature Page

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AMH-II, LLC

By:

 

/s/ Thomas L. Pearson

 

Name:

 

Thomas L. Pearson

 

Title:

  Secretary ALLIANCE RESOURCE HOLDINGS II, INC.

By:

 

/s/ Thomas L. Pearson

 

Name:

 

Thomas L. Pearson

 

Title:

  Secretary

Amendment to Omnibus Agreement

Signature Page