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 October 31, 2004 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 Mutual Funds, Inc.	Treasurer, The Hennessy Mutual Funds, Inc.
Dated: 1/10/05	Dated: 1/10/05

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 the Securities Exchange Act of 1934.