PRUDENTIAL BACHE SPECIAL MONEY MARKET FUND
24F-2NT, 1995-08-29
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                                                  August 29, 1995

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

                     Re:   Rule 24f-2 Notice for Prudential Special Money Market
               Fund - File No. 811-5951

Ladies and Gentlemen:

     This Notice is filed on behalf of Prudential Special Money Fund pursuant to
the requirements of Rule 24f-2 under the Investment Company Act of 1940.

          1.   Fiscal year for which notice is filed:  6/30/95.

          2.    Number  of shares registered under the Securities  Act  of  1933
          other than pursuant to Rule 24f-2 but which remained unsold as of  the
          beginning of the fiscal year (7/1/94): None.

          3.    The  number  of shares registered during the fiscal  year  ended
          6/30/95 other than pursuant to Rule 24f-2: None.

          4.    The number of shares sold* during the fiscal year ended 6/30/95:
          1,731,707,729.

          5.   The number of shares sold during the fiscal year ended 6/30/95 in
          reliance upon Rule 24f-2: 1,731,707,729.

      Pursuant to the requirements of Rule 24f-2, a fee in the amount of $   - 0
- -       has been paid in connection with this filing.



                                   Yours truly,

                                   /s/ S. Jane Rose
                                   S. Jane Rose
                                   Secretary

Enclosures

*Calculation of Fee           No. of Shares       Dollar Amount

Shares sold                    1,731,707,729      $ 1,731,707,729
Shares redeemed               (1,851,454,305)     $(1,851,454,305)
Net of sales for
 calculation of fee             (119,746,576)     $ (119,746,576)
Fee at 1/29 of 1%                                 $    - 0 -









                                             August 29, 1995


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

          Re:  Prudential Special Money Market Fund
               File No. 811-5951

Ladies and Gentlemen:

      On  behalf  of  Prudential Special Money Market Fund, the following  is  a
submission  of  a  Notice  and  related  opinion  of  counsel  pursuant  to  the
requirements  of  Rule  24f-2  of the Investment Company  Act  of  1940.   These
documents are being filed via the EDGAR System.

      If  you  have  any questions relating to the foregoing,  please  call  the
undersigned at (212) 214-3118.

                                   Yours truly,


                                   /s/Ellyn C. Acker
                                   Ellyn C. Acker
                                   Assistant Secretary



Enclosures






SMMF\24F-2.LTR




              PRUDENTIAL SPECIAL MONEY MARKET FUND
                    TREASURER'S CERTIFICATE


      The  undersigned,  Treasurer of Prudential Special Money  Market  Fund,  a

Maryland Corporation (the "Fund"), does hereby certify as follows:

          1.    For  the  fiscal  year  ended June 30,  1995,  the  Fund  issued

          1,731,707,729 shares of Common Stock.

          2.   In respect of the issuance of such 1,731,707,729 shares, the Fund

          received cash consideration of 1,731,707,729.

          3.    With  respect  to  each share issued,  the  Fund  received  cash

          consideration not less than the net asset value per share on the  date

          issued.

          4.    To  the  best of my knowledge and belief, the Fund  is  in  good

          standing in the State of Maryland.

          5.    At no time during the fiscal year ended June 30, 1995 were there

          issued  and  outstanding more shares of the Fund's Common  Stock  than

          authorized by the Articles of Incorporation.

      In  Witness  Whereof, I have hereunto signed my name as Treasurer  of  the

Fund.



Date:  August 25, 1995

                                   /s/ Eugene S. Stark
                                   Eugene S. Stark




Securities and Exchange Commission
August 19, 1993
Page 1





                            GARDNER, CARTON & DOUGLAS
                            Suite 3400 - Quaker Tower
                             321 North Clark Street
                          Chicago, Illinois  60610-4795
                                 (312) 644-3000
                           Telecopier:  (312) 644-3381
                                        


                                 August 28, 1995

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

    Re:  Prudential-Bache Special Money Market Fund, Inc.
    (d/b/a Prudential Special Money Market Fund), Money Market Series
    Rule 24f-2 Notice to Form N-1A Registration Statement, File No. 811-5951

Ladies and Gentlemen:

     As  counsel  for  Prudential-Bache Special Money Market Fund,  Inc.,  d/b/a
Prudential  Special Money Market Fund, a Maryland corporation (the  "Fund"),  we
have  examined the proceedings taken and being taken with respect to the  Notice
filed  by  the Fund pursuant to Rule 24f-2 under the Investment Company  Act  of
1940  (the  "Act"), making definite in number the shares registered pursuant  to
that Rule for the fiscal year ended June 30, 1995.

    We have examined all instruments, documents and records which, in our 
opinion, were  necessary of examination for the purpose of rendering this
opinion.  Based upon  such  examination, we are of the opinion that the
120,036,576  shares  of common  stock,  $.001 par value per share, which were
registered  in  indefinite number  pursuant  to  Rule 24f-2 under the Act
were, when issued  by  the  Fund, validly authorized and issued, fully paid
and non-assessable.

    We hereby consent to the filing of this opinion pursuant to Rule 24f-2 and
to the reference to us in the Notice filed herewith.

                       Very truly yours,

                 /s/ Gardner, Carton & Douglas

                   Gardner, Carton & Douglas

PHD/KJF/cav



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