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                                                                 EXHIBIT h(1)(e)
                    AMENDMENT NUMBER 4 TO THE TRANSFER AGENCY
                              AND SERVICE AGREEMENT
This Amendment, dated as of July 1, 2000 is made to the Transfer Agency and
Service Agreement dated September 8, 1998, as amended (the "Agreement") between
AIM Series Trust (the "Fund") and A I M Fund Services, Inc. ("AFS") pursuant to
Article 10 of the Agreement.
Paragraph 1 of the Fee Schedule is hereby deleted in its entirety and replaced
with the following:
"1.      For performance by the Transfer Agent pursuant to this Agreement, the
         Fund agrees on behalf of each of the Portfolios to pay the Transfer
         Agent an annualized fee for shareholder accounts that are open during
         any monthly period as set forth below, and an annualized fee of $ .70
         per shareholder account that is closed during any monthly period. Both
         fees shall be billed by the Transfer Agent monthly in arrears on a
         prorated basis of 1/12 of the annualized fee for all such accounts.
                                                        Per Account Fee
         Fund Type                                         Annualized
         ---------                                      ---------------
                                                     
         Class A, B and C
         Non-Daily Accrual Funds                             $15.20
         Class A, B and C
         Monthly Dividend and Daily Accrual Funds             16.20"
Paragraph 4 of the Fee Schedule is hereby deleted in its entirety and replaced
with the following:
"4.   Other Fees
      ▇▇▇ Annual Maintenance Fee    $10 per ▇▇▇ account per year (paid by
                                    investor per tax I.D. number).
      Balance Credit                The total fees due to the Transfer Agent
                                    from all funds affiliated with the Fund
                                    shall be reduced by an amount equal to the
                                    investment income earned by the Transfer
                                    Agent on the DDA balances of the
                                    disbursement accounts for those funds.
      Remote Services Fee           $3.60 per open account per year, payable
                                    monthly and $1.80 per closed account per
                                    year, payable monthly."
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All other terms and provisions of the Agreement not amended herein shall remain
in full force and effect, except that Amendment Number 1 dated July 1, 1999 is
hereby terminated.
                                             AIM SERIES TRUST
                                             By:  /s/ ▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇
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                                                       President
ATTEST:
/s/ ▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇
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Vice President
                                             A I M FUND SERVICES, INC.
                                             By:  /s/ ▇▇▇▇ ▇. ▇▇▇▇▇
                                                  ------------------------------
                                                       President
ATTEST:
/s/ ▇▇▇▇ ▇. ▇▇▇▇
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Assistant Secretary