Exhibit b(c)

SECOND AMENDMENT TO

BYLAWS

OF AIM COMBINATION STOCK & BOND FUNDS

Adopted effective September 15, 2004

The Bylaws of AIM Combination Stock & Bond Funds (the “Trust”), adopted effective July 29, 2003, (the “Bylaws”), are hereby amended as follows:

1. A new Section 7 is hereby added to Article II, such new Section 7 to read in its entirety as follows:

“Section 7. Chair; Vice Chair. The Board of Trustees shall have a Chair, who shall be a Trustee who is not an “interested person,” as such term is defined in the 1940 Act. The Chair shall be elected by a majority of the Trustees, including a majority of the Trustees who are not “interested persons,” as such term is defined in the 1940 Act. The Board of Trustees may also have a Vice Chair, who shall be a Trustee. The Vice Chair shall be elected by a majority of the Trustees, including a majority of the Trustees who are not “interested persons,” as such term is defined in the 1940 Act. The Chair shall preside at all meetings of the Shareholders and the Board of Trustees, if the Chair is present, and shall approve the agendas of all meetings of the Shareholders and the Board of Trustees. The Chair shall have such other powers and duties as shall be determined by the Boards of Trustees, and shall undertake such other assignments as may be requested by the Boards of Trustees. If the Chair shall not be present, the Vice Chair, if any, shall preside at all meetings of the Shareholders and the Board of Trustees, if the Vice Chair is present. The Vice Chair shall have such other powers and duties as shall be determined by the Chair or the Boards of Trustees, and shall undertake such other assignments as may be requested by the Chair or the Boards of Trustees.”

2. Section 1 of Article III is hereby amended and restated to read in its entirety as follows:

“Section 1. Executive Officers. The initial executive officers of the Trust shall be elected by the Board of Trustees as soon as practicable after the organization of the Trust. The executive officers shall include a President, one or more Vice Presidents (the number thereof to be determined by the Board of Trustees), a Secretary and a Treasurer. The Board of Trustees may also in its discretion appoint Assistant Vice Presidents, Assistant Secretaries, Assistant Treasurers, and other officers, agents and employees, who shall have such authority and perform such duties as the Board may determine. The Board of Trustees may fill any vacancy which may occur in any office. Any two offices, except for those of President and Vice President, may be held by the same person, but no officer shall execute, acknowledge or verify any instrument on behalf of the Trust in more than one capacity, if such instrument is required by law or by these Bylaws to be executed, acknowledged or verified by two or more officers.”

3. Section 3 of Article III is hereby amended and restated to read in its entirety as follows:

“Section 3. President. The President shall be the chief executive officer of the Trust and, subject to the Board of Trustees, shall generally manage the business and affairs of the Trust. If both the Chair and the Vice Chair are absent, or if the Chair is absent and there is no Vice Chair, the President shall, if present, preside at all meetings of the Shareholders and the Board of Trustees.”

4. Section 4 of Article III is hereby deleted in its entirety and remaining Sections 5, 6, 7, 8, 9 and 10 of Article III are hereby renumbered as Sections 4, 5, 6, 7, 8 and 9, respectively.

5. New Section 4 (formerly Section 5) of Article III is hereby amended and restated to read in its entirety as follows:

“Section 4. Vice Presidents. One or more Vice Presidents shall have and exercise such powers and duties of the President in the absence or inability to act of the President, as may be assigned to them, respectively, by the Board of Trustees or, to the extent not so assigned, by the President. In the absence or inability to act of the President, the powers and duties of the President not otherwise assigned by the Board of Trustees or the President shall devolve upon the Vice Presidents in the order of their election.”

6. Section 9(a) of Article IV is hereby amended and restated to read in its entirety as follows:

“Section 9. Organization of Meetings.

(a) The meetings of the Shareholders shall be presided over by the Chair, or if the Chair shall not be present, by the Vice Chair, if any, or if the Vice Chair shall not be present or if there is no Vice Chair, by the President, or if the President shall not be present, by a Vice President, or if no Vice President is present, by a chair appointed for such purpose by the Board of Trustees or, if not so appointed, by a chair appointed for such purpose by the officers and Trustees present at the meeting. The Secretary of the Trust, if present, shall act as Secretary of such meetings, or if the Secretary is not present, an Assistant Secretary of the Trust shall so act, and if no Assistant Secretary is present, then a person designated by the Secretary of the Trust shall so act, and if the Secretary has not designated a person, then the meeting shall elect a secretary for the meeting.”

7. Capitalized terms not specifically defined herein shall have the meanings ascribed to them in the Trust’s Agreement and Declaration of Trust, as amended.

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