SECOND AMENDMENT TO THE AMENDED AND RESTATED

Exhibit 10.51

SECOND AMENDMENT

TO THE AMENDED AND RESTATED

ALLIANCE RESOURCE MANAGEMENT GP, LLC

LONG-TERM INCENTIVE PLAN

WHEREAS, Alliance Resource Management GP, LLC (the “Company”) maintains the Alliance Resource Management GP, LLC Amended and Restated Long-Term Incentive Plan (the “Plan”); and

WHEREAS, the Company desires to transfer sponsorship of the Plan to Alliance Coal, LLC (“Coal”); and

WHEREAS, Coal desires to accept the transfer of the sponsorship of the Plan;

NOW, THEREFORE, effective as of May 15, 2006 sponsorship of the Plan is hereby transferred to Coal and the Plan is amended by replacing “Alliance Resource Management GP, LLC” with “Alliance Coal, LLC” in all places in the Plan in which “Alliance Resource Management GP, LLC” appears, including, without limitation, in the title of the Plan.

EXECUTED this 24^th day of January, 2007, effective for all purposes as of May 15, 2006.