EX.99.906CERT

        CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT
        ---------------------------------------------------------------

     Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each of the
undersigned officers of The Hennessy Mutual Funds, Inc., does hereby certify, to
such officer's knowledge, that the report on Form N-CSR of The Hennessy Mutual
Funds, Inc. for the period ended April 30, 2006 fully complies with the
requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934,
as applicable, and that the information contained in the Form N-CSR fairly
presents, in all material respects, the financial condition and results of
operations of The Hennessy Mutual Funds, Inc. for the stated period.

/s/ Neil J. Hennessy                    /s/ Teresa M. Nilsen
- -----------------------                 -----------------------
Neil J. Hennessy                        Teresa M. Nilsen
President, The Hennessy                 Treasurer, The Hennessy
Mutual Funds, Inc.                      Mutual Funds, Inc.

Dated:   July 7, 2006                   Dated:  July 7, 2006
       ----------------                       -----------------

This statement accompanies this report on Form N-CSR pursuant to Section 906 of
the Sarbanes-Oxley Act of 2002 and shall not be deemed as filed by The Hennessy
Mutual Funds, Inc. for purposes of Section 18 of the Securities Exchange Act of
1934.