EXHIBIT l(1)(b)

[AIM LOGO APPEARS HERE]
--Registered Trademark--
11 Greenway Plaza, Suite 100
Houston, TX 77046-1173
713-626-1919
AIM Advisors, Inc.


                                                              December 28, 2001

Board of Trustees
AIM Investment Securities Funds
11 Greenway Plaza, Suite 100
Houston, Texas 77046-1173

Re:      Initial Capital Investment in New Portfolio of
         AIM Investment Securities Funds (The "Fund")

Ladies and Gentlemen:

         We are purchasing shares of the Fund for the purpose of providing
initial investment for a new investment portfolio of the Fund. The purpose of
this letter is to set out our understanding of the conditions of and our
promises and representations concerning this investment.

We hereby agree to purchase shares equal to the following dollar amount for the
portfolio:





                   FUND                                            AMOUNT                       DATE
                   ----                                            ------                       ----
                                                                                     
AIM Total Return Bond Fund - Class A Shares                        $ 10.00                 December 28, 2001
AIM Total Return Bond Fund - Class B Shares                        $ 10.00                 December 28, 2001
AIM Total Return Bond Fund - Class C Shares                        $ 10.00                 December 28, 2001
AIM Total Return Bond Fund - Class A Shares                        $1,000,000.00           December 31, 2001
AIM Total Return Bond Fund - Class B Shares                        $1,000,000.00           December 31, 2001
AIM Total Return Bond Fund - Class C Shares                        $1,000,000.00           December 31, 2001




         We understand that the initial net asset value per share for the
portfolio named above will be $10.

         We hereby represent that we are purchasing these shares solely for our
own account and solely for investment purposes without any intent of
distributing or reselling said shares. We further represent that disposition of
said shares will only be by direct redemption to or repurchase by the Fund.

         We further agree to provide the Fund with at least three days' advance
written notice of any intended redemption and agree that we will work with the
Fund with respect to the amount of such redemption so as not to place a burden
on the Fund and to facilitate normal portfolio management of the Fund.

                                            Sincerely yours,

                                            A I M ADVISORS, INC.


                                            By:  /s/ ROBERT H. GRAHAM
                                                 -------------------------------
                                                     Robert H. Graham
                                                     President

cc:      Sara Ehlert-Gerke
         David Hessel
         Gary Trappe
         Bobbie Stafford-Garza