HENNESSY FUNDS INC
497J, 1998-11-04
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                                                              November 3, 1998


VIA EDGAR SYSTEM

Securities and Exchange Commission
450 Fifth Street, N.W.
Judiciary Plaza
Washington, DC  20549

             Re: Hennessy Funds, Inc.
                 File Nos. 333-00227 and 811-07493
                 Rule 497(j) Certification - Statement of Additional Information

Ladies & Gentlemen: 

          The undersigned  officer of Hennessy Funds,  Inc. (the "Company") does
hereby certify pursuant to Rule 497(j)  promulgated  under the Securities Act of
1933, as amended:

          1. that the form of statement  of  additional  information  that would
have been filed under paragraph (c) of Rule 497 promulgated under the Securities
Act of 1933,  as  amended,  would  not have  differed  from  that  contained  in
Post-Effective  Amendment No. 4 to Form N-1A Registration Statement filed by the
Company  on  October  30,  1998,  which is the  most  recent  amendment  to such
registration statement; and

          2. that the text of Post-Effective  Amendment No. 4 was filed with the
Securities  and  Exchange  Commission  by direct  transmittal  through the EDGAR
system on October 30, 1998.

                                            Very truly yours,

                                            HENNESSY FUNDS, INC.



                                            By:      /s/ Teresa M. Nilsen
                                                     Teresa M. Nilsen
                                                     Vice President



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