AMENDMENT NO. 1

   1
                                                                 EXHIBIT h(1)(b)


                                 AMENDMENT NO. 1

                      TRANSFER AGENCY AND SERVICE AGREEMENT

         The Transfer Agency and Service Agreement (the "Agreement"), dated as
of September 8, 1998, by and between AIM Growth Series, a Delaware business
trust, and A I M Fund Services, Inc., a Delaware corporation, is hereby amended
as follows (terms used herein but not otherwise defined herein have the meaning
ascribed them in the Agreement):

1)       Section 1. of the Fee Schedule to the Agreement 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 Annual/Semi-Annual Dividends                             $24.85*
Class A Quarterly & Monthly Dividend                              24.85*
Class A Daily Accrual                                             24.85*
Class B                                                           24.85*
Class C                                                           24.85*
Advisor Class                                                     24.85*

*    This fee includes all out of pocket expenses, the annualized
     credit, Consumer Price Index increase, Balance Credit and Remote Services
     Fee discussed below. Currently, therefore, paragraphs 2,3, and 5 below do
     not apply. Paragraph 4 does not apply for 1998, however the XXX Annual
     Maintenance Fee will be charged beginning in 1999."

     All other terms and provisions of the Agreement not amended herein shall
remain in full force and effect.

Dated:  May 3, 1999

                                        AIM GROWTH SERIES


Attest: /s/ XXXXXX X. XXXX              By: /s/ XXXXXX X. XXXXXX
       -----------------------------       -----------------------------------
       Assistant Secretary                  Xxxxxx X. Xxxxxx
                                            President
(SEAL)

                                        A I M FUND SERVICES, INC.


Attest: /s/ XXXX X. XXXX                By: /s/ XXXX XXXXXXXX
       -----------------------------        ----------------------------------
       Assistant Secretary                  Xxxx Xxxxxxxx
                                            President
(SEAL)