ALLIANCE LIMITED MATURITY GOVERNMENT FUND INC
24F-2NT, 2000-02-11
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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 Limited Maturity Government Fund, 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:

      811-06627

      Securities Act File Number:

      33-47031

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

      November 30, 1999

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):                       $156,089,085

      (ii)   Aggregate price of securities
             redeemed or repurchased during the
             fiscal year:                            $185,306,222

      (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:                             $344,960,793

      (iv)   Total available redemption credits
             [add Items 5(ii) and 5(iii)]:           $530,267,015

      (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)]:                ($374,177,930)

      (vii)  Multiplier for determining
             registration fee (See Instruction
             C.9):                                      x .000264

      (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:
      930,172.  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: -0-




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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


                           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: February 9, 2000

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




















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