ALLIANCE MULTI MARKET STRATEGY TRUST INC
24F-2NT, 1999-01-13
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                          UNITED STATES
               SECURITIES AND EXCHANGE COMMISSION
                      Washington, DC 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:

    Alliance Multi-Market Strategy Trust, Inc.
    1345 Avenue of the Americas
    New York, NY 10105


2.  The name of each series or class of securities for which this
    Form is filed (If the Form is being filed for all series and
    classes of securities of the issuer, check the box but do not
    list series or classes):                       /X/


3.  Investment Company Act File Number:

    811-06251

    Securities Act File Number:

    33-39350

4(a).      Last day of fiscal year for which this Form is filed:

           October 31, 1998


4(b)./ /   Check box if this Form is being filed late (i.e., more
           than 90 calendar days after the end of the issuer's
           fiscal year).  (See Instruction A.2)


Note: If the Form is being filed late, interest must be paid on
the registration fee due.


4(c)./ /   Check box if this is the last time the issuer will be
           filing this Form.



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5.  Calculation of registration fee: 

    (i)    Aggregate sale price of securities
           sold during the fiscal year pursuant
           to section 24(f):                                 $-0-

    (ii)   Aggregate price of securities redeemed
           or repurchased during the fiscal year:     $28,250,072

    (iii)  Aggregate price of securities redeemed
           or repurchased during any prior fiscal
           year ending no earlier than October 11,
           1995 that were not previously used to
           reduce registration fees payable to the
           Commission:                                $40,062,823

    (iv)   Total available redemption credits
           [add Items 5(ii) and 5(iii)]:             -$68,312,895

    (v)    Net sales - if Item 5(i) is greater
           than Item 5(iv) [subtract Item 5(iv)
           from Item 5(i)]:                                  $-0-

    (vi)   Redemption credits available for use
           in future years - if Item 5(i) is less
           than Item 5(iv) [subtract Item 5(iv)
           from Item 5(i)]:                         $(68,312,895)

    (vii)  Multiplier for determining registration
           fee (See Instruction C.9):                    x.000278

    (viii) Registration fee due [multiply Item 5(v)
            by Item 5(vii)] (enter "0" if no fee is
           due):                                            =$-0-

6.  Prepaid Shares

    If the response to item 5(i) was determined by deducting an
    amount of securities that were registered under the
    Securities Act of 1933 pursuant to rule 24e-2 as in effect
    before October 11, 1997, then report the amount of securities
    (number of shares or other units) deducted here: 4,317,049.
    If there is a number of shares or other units that were
    registered pursuant to rule 24e-2 remaining unsold at the end
    of the fiscal year for which this form is filed that are
    available for use by the issuer in future fiscal years, then
    state that number here: 68,296,817.






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7.  Interest due - if this Form is being filed more than 90 days
    after the end of the issuer's fiscal year (see Instruction
    D):

                                                   +$-0-


8.  Total of the amount of the registration fee 
    due plus any interest due [line 5(viii)
    plus line 7]:

                                                   =$-0-


9.  Date the registration fee and any interest payment was sent
    to the Commission's lockbox depository:



    Method of Delivery:

              / /  Wire Transfer

              / /  Mail or other means





























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                           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.


By (Signature and Title)* /s/Andrew L. Gangolf
                                                
                             Andrew L. Gangolf
                             Assistant Secretary

Date: January 12, 1999

*Please print the name and title of the signing officer below the
signature.





































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00250182.AX6



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