Exhibit 32.1

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Alliance Resource Partners, L.P. (the
"Partnership") on Form 10-Q for the quarter ended March 31, 2004 as filed with
the Securities and Exchange Commission on the date hereof (the "Report"), I,
Joseph W. Craft III, President and Chief Executive Officer of Alliance Resource
Management GP, LLC, the managing general partner of the Partnership, certify,
pursuant to 18 U.S.C. section 1350, as adopted pursuant to section 906 of the
Sarbanes-Oxley Act of 2002, that:

      (1)   The Report fully complies with the requirements of section 13(a) or
            15(d) of the Securities Exchange Act of 1934; and

      (2)   The information contained in the Report fairly presents, in all
            material respects, the financial condition and result of operations
            of the Partnership.

      By: /s/ Joseph W. Craft III
          ----------------------------------------
      Joseph W. Craft III
      President and Chief Executive Officer
      of Alliance Resource Management GP, LLC
      (the managing general partner of Alliance Resource Partners, L.P.)

      Date:  May 7, 2004

The foregoing certification is being furnished solely pursuant to 18 U.S.C.
Section 1350 and is not being filed as part of the Report or as a separate
document. A signed original of this written statement required by Section 906
has been provided to the Partnership and will be retained by the Partnership and
furnished to the Securities and Exchange Commission or its staff upon request.