SECOND AMENDMENT TO THE AMENDED AND RESTATED

Exhibit 10.55

SECOND AMENDMENT

TO THE AMENDED AND RESTATED

ALLIANCE RESOURCE MANAGEMENT GP, LLC

DEFERRED COMPENSATION PLAN FOR DIRECTORS

WHEREAS, Section 5.4 of the Alliance Amended and Restated Alliance Resource Management GP, LLC Deferred Compensation Plan for Directors (the “Plan”) provides that it may be amended by the Compensation Committee of the Board of Directors of Alliance Resource Management GP, LLC (the “Compensation Committee”); and

WHEREAS, the Compensation Committee has approved amending the Plan as set forth herein.

NOW, THEREFORE, the Plan is hereby amended as follows:

4.4 Payment of Accounts. Upon the earlier of a Participant’s Termination or Designated Payment Date, as applicable, the Company shall pay to such Participant (or to his or her Beneficiary in the case of the Participant’s death) an amount of cash equal to the Fair Market Value of the Phantom Units then credited to his or her Account. Payment of Accounts shall be made as soon as reasonably practical, and not later than thirty (30) days, following the Participant’s Termination or Designated Payment Date, whichever is applicable.

4.5 Unforeseeable Emergency. The Committee may accelerate the payment of all or part of a Participant’s Account upon its determination that the Participant has incurred an “unforeseeable emergency,” as defined in Section 409A of the Internal Revenue Code, to the extent such accelerated payment would not result in the additional 20% tax being imposed on the Director by Section 409A. In addition, the Committee may, to the extent permitted by Section 409A, provide that the director’s deferral election shall automatically terminate upon any withdrawal due to an unforeseeable emergency.

5.4 Termination and Amendment. The Board may from time to time amend, suspend, or terminate the Plan, in whole or in part, and if the Plan is suspended or terminated, the Board may reinstate any or all of its provisions. The Committee may also amend the Plan; provided, however, it may not suspend or terminate the Plan, or substantially increase the

obligations of the Company under the Plan or expand the classification of employees who are eligible to participate in the Plan. No amendment, suspension or termination of the Plan may impair the right of a Participant or his or her Beneficiary to receive the benefit accrued hereunder prior to the effective date of such amendment, suspension or termination.

Upon termination of the Plan, all Accounts shall be paid subject to the following: (1) all arrangements of the Company and those entities that would be aggregated with the Company for purposes of Section 409A of the Code, if the same Director participated in all of the arrangements, are terminated, (2) no payment other than payments that would be payable under the terms of the arrangements if the termination had not occurred are made within 12 months of the termination of the arrangements, (3) all payments are made within 24 months of the termination of the arrangements, and (4) the Company and such affiliates do not, within five years following the termination, adopt a new arrangement that would be aggregated within any of the terminated arrangements if the same Director participated in both arrangements.

In addition to the above, all Accounts shall be paid, as determined by the Committee, upon the termination of the Plan within 30 days preceding or 12 months following a “change in control event” (as defined in regulations under Section 409A), provided that all substantially similar arrangements of the Company and such affiliates are terminated and all participants under all substantially similar arrangements are required to receive all amounts of compensation deferred under the terminated arrangements within 12 months of the termination of the arrangements.

Notwithstanding anything herein to the contrary, the Plan shall be construed and operated in such manner as necessary to comply with Section 409A and the applicable regulations issued thereunder.

EXECUTED and EFFECTIVE this 29^th day of January 2008.

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