PRUDENTIAL BACHE SPECIAL MONEY MARKET FUND
24F-2NT, 1996-08-27
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            U.S. SECURITIES AND EXCHANGE COMMISSION
                    Washington, D.C.  20549

                           FORM 24F-2
                Annual Notice of Securities Sold
                     Pursuant to Rule 24f-2

    Read instructions at end of Form before preparing Form.
                     Please print or type.



     1.   Name and address of issuer:  Prudential Special
Money Market Fund, Inc., One Seaport Plaza, New York, New
York  10292.

     2.   Name of each series or class of funds for which
this  notice is filed:  The Fund offers one class of shares.
     3.   Investment Company Act File Number:  811-5951.
          Securities Act File Number:  33-31603.

     4.   Last day of fiscal year for which this notice is
filed:  June 30, 1996.

     5.   Check box if this notice is being filed more than
180 days after the close of the issuer's fiscal year for
purposes of reporting securities sold after the close of
the fiscal year but before termination of the issuer's  24f-
2 declaration:
                                                       [ ]

     6.   Date of termination of issuer's declaration under
rule  24f-2(a)(1), if applicable (see instruction A.6):

     7.   Number and amount of securities of the same class
or series which had been registered under the Securities Act
of 1933 other than pursuant to rule 24f-2 in a prior fiscal
year, but which remained unsold at the beginning of the
fiscal year: None.

     8.   Number and amount of securities registered during
the fiscal year other than pursuant to rule 24f-2:
120,036,576/$120,036,576

     9.   Number and aggregate sale price of securities sold
during the fiscal year: 1,787,450,626/$1,787,450,626

    10.   Number and aggregate sale price of securities sold
during  the fiscal year in reliance upon registration
pursuant to  rule 24f-2:1,787,450,626/$1,787,450,626


    11.   Number and aggregate sale price of securities
issued during the fiscal year in connection with dividend
reinvestment plans, if applicable (see instruction B.7):
13,336,273/$13,336,273

    12.   Calculation of registration fee:

          (i)  Aggregate sale price of securities
               sold during the fiscal year in
               reliance on rule 24f-2 (from item 10):
1,787,450,626

        (ii)  Aggregate price of shares issued in
              connection with dividend reinvestment
              plans (from item 11, if applicable):     +
13,336,273

       (iii)  Aggregate price of shares redeemed or
              repurchased during the fiscal year
              (if applicable):                         -
1,857,717,889

        (iv)  Aggregate price of shares redeemed or
              repurchased and previously applied
              as a reduction to filing fees
              pursuant to rule 24e-2
              (if applicable):                         +
0

         (v)  Net aggregate price of securities
              sold and issued during the fiscal
              year in reliance of rule 24f-2
              [line (i), plus line (ii), less
              line (iii), plus line (iv)]
              (if applicable):
(56,930,990)

        (vi)  Multiplier prescribed by section
              6(b) of the Securities Act of 1933
              or other applicable law or regulation
              (see instruction C.6):                   x
1/2900

       (vii)  Fee due [line (i) or line (v)
              multiplied by line (vi)]:
0


Instructions:  Issuers should complete lines (ii), (iii),
(iv) and (v) only if the form is being filed within 60 days
after the close of the issuer's fiscal year.  See
Instruction C.3.

    13.   Check box if fees are being remitted to the
Commission's lockbox depository as described in section 3a
of the Commission's Rules of Informal and Other Procedures
(17 CFR 202.3a).
                                              [ ]

          Date of mailing or wire transfer of filing fees to
the             Commission's lockbox depository:

                           SIGNATURES

     This report has been signed below by the following
persons on behalf of the issuer and in the capacities and on
the dates indicated.

                              /s/S. Jane Rose
                              By (S. Jane Rose, Secretary)

     Date:  August 27, 1996














smm8-96.NOT


Securities and Exchange Commission
August 19, 1993
Page 2


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


                                 August 26, 1996

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

     Re:  Prudential Special Money Market Fund, Inc.
          Rule 24f-2 Notice to Form N-1A Registration
Statement, File No. 811-5951

Ladies and Gentlemen:

      As  counsel for Prudential Special Money Market  Fund,
Inc.,  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, 1996.

     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 1,787,450,626 of
common  stock,  $.001  par  value  per  share,  which   were
registered  in  indefinite number and sold  in  reliance  on
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/MAM/ldh



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