PRUDENTIAL SPECIAL MONEY MARKET FUND INC, 497J, 1997-08-29

PRUDENTIAL SPECIAL MONEY MARKET FUND INC
497J, 1997-08-29

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                   PRUDENTIAL SPECIAL MONEY MARKET FUND, INC.
                         GATEWAY CENTER THREE, 9TH FLOOR
                         NEWARK, NEW JERSEY  07102-4077


                                        August 29, 1997


VIA EDGAR
- ---------

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

ATTN:     Office of Filings, Information and Consumer Services

Re:       Prudential Special Money Market Fund, Inc.
          File Nos. 33-31603 and 811-5951

Dear Sir/Madam:

     Pursuant to Rule 497(j) under the Securities Act of 1933, as amended,
please accept this letter as certification that the prospectus and statement of
additional information for the above-referenced Fund does not differ from that
contained in Post-Effective Amendment No. 10 to the Fund's Registration
Statement on Form N-1A, which was filed electronically on August 26, 1997.

     Any comments on this filing should be directed to Deborah A. Docs at (201)
367-7521.

     Please return an electronic transmittal as evidence of your receipt of this
filing.

                                        Sincerely yours,

                                        /s/ Thomas A. Early
                                        ----------------------------------------
                                        Thomas A. Early
                                        Vice President