<PAGE>   1
 
                                                                      EXHIBIT 24
 
                AMERICAN GENERAL CORPORATION: BOARD OF DIRECTORS
 
Date:     February 6, 1997
Subject:  Form 10-K; Limited Power of Attorney for
 
Purpose.  The purpose of this limited power of attorney is to authorize certain
--------  officers of the company to execute, on behalf of the undersigned
          person, the company's 1996 annual report on Form 10-K, with such
          amendments thereto as may be necessary or appropriate, together with
          any and all exhibits and other related documents, and to file the 
          Form 10-K with the SEC.
 
                           LIMITED POWER OF ATTORNEY
 
     WHEREAS, AMERICAN GENERAL CORPORATION, a Texas corporation (company), will
file with the Securities and Exchange Commission (Commission) under Section 13
of the Securities Exchange Act of 1934, as amended (Act), its annual report on
Form 10-K for the fiscal year ended December 31, 1996 (Form 10-K), with such
amendments thereto as may be necessary or appropriate, together with any and all
exhibits and other documents related thereto;
 
     NOW, THEREFORE, the undersigned in his/her capacity as a director or
officer or both, as the case may be, of the company does hereby appoint JON P.
NEWTON, CARL J. SANTILLO, and JOHN A. ADKINS, and each of them, severally,
his/her true and lawful attorney or attorneys-in-fact with or without the others
and with full power of substitution and resubstitution, to execute in his/her
name, place, and stead, in his/her capacity as a director or officer or both, as
the case may be, of the company, the Form 10-K and any and all amendments
thereto as said attorneys-in-fact or any of them shall deem necessary or
appropriate, together with all instruments necessary or incidental in connection
therewith, and to file the same or cause the same to be filed with the
Commission. Each of said attorneys-in-fact shall have full power and authority
to do and perform in the name and on behalf of the undersigned, in any and all
capacities, every act whatsoever necessary or desirable in connection with the
Form 10-K, as fully and for all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts of
said attorneys-in-fact and each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument this sixth
day of February, 1997.
 
                                                  /s/ J. EVANS ATTWELL
                                            ------------------------------------
                                                      J. Evans Attwell
<PAGE>   2
 
                                                                      EXHIBIT 24
 
                AMERICAN GENERAL CORPORATION: BOARD OF DIRECTORS
 
Date:     February 6, 1997
Subject:  Form 10-K; Limited Power of Attorney for
 
Purpose.  The purpose of this limited power of attorney is to authorize certain
--------  officers of the company to execute, on behalf of the undersigned
          person, the company's 1996 annual report on Form 10-K, with such
          amendments thereto as may be necessary or appropriate, together with
          any and all exhibits and other related documents, and to file the 
          Form 10-K with the SEC.
 
                           LIMITED POWER OF ATTORNEY
 
     WHEREAS, AMERICAN GENERAL CORPORATION, a Texas corporation (company), will
file with the Securities and Exchange Commission (Commission) under Section 13
of the Securities Exchange Act of 1934, as amended (Act), its annual report on
Form 10-K for the fiscal year ended December 31, 1996 (Form 10-K), with such
amendments thereto as may be necessary or appropriate, together with any and all
exhibits and other documents related thereto;
 
     NOW, THEREFORE, the undersigned in his/her capacity as a director or
officer or both, as the case may be, of the company does hereby appoint JON P.
NEWTON, CARL J. SANTILLO, and JOHN A. ADKINS, and each of them, severally,
his/her true and lawful attorney or attorneys-in-fact with or without the others
and with full power of substitution and resubstitution, to execute in his/her
name, place, and stead, in his/her capacity as a director or officer or both, as
the case may be, of the company, the Form 10-K and any and all amendments
thereto as said attorneys-in-fact or any of them shall deem necessary or
appropriate, together with all instruments necessary or incidental in connection
therewith, and to file the same or cause the same to be filed with the
Commission. Each of said attorneys-in-fact shall have full power and authority
to do and perform in the name and on behalf of the undersigned, in any and all
capacities, every act whatsoever necessary or desirable in connection with the
Form 10-K, as fully and for all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts of
said attorneys-in-fact and each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument this sixth
day of February, 1997.
 
                                                  /s/ BRADY F. CARRUTH
                                            ------------------------------------
                                                      Brady F. Carruth
<PAGE>   3
 
                                                                      EXHIBIT 24
 
                AMERICAN GENERAL CORPORATION: BOARD OF DIRECTORS
 
Date:     February 6, 1997
Subject:  Form 10-K; Limited Power of Attorney for
 
Purpose.  The purpose of this limited power of attorney is to authorize certain
--------  officers of the company to execute, on behalf of the undersigned
          person, the company's 1996 annual report on Form 10-K, with such
          amendments thereto as may be necessary or appropriate, together with
          any and all exhibits and other related documents, and to file the 
          Form 10-K with the SEC.
 
                           LIMITED POWER OF ATTORNEY
 
     WHEREAS, AMERICAN GENERAL CORPORATION, a Texas corporation (company), will
file with the Securities and Exchange Commission (Commission) under Section 13
of the Securities Exchange Act of 1934, as amended (Act), its annual report on
Form 10-K for the fiscal year ended December 31, 1996 (Form 10-K), with such
amendments thereto as may be necessary or appropriate, together with any and all
exhibits and other documents related thereto;
 
     NOW, THEREFORE, the undersigned in his/her capacity as a director or
officer or both, as the case may be, of the company does hereby appoint JON P.
NEWTON, CARL J. SANTILLO, and JOHN A. ADKINS, and each of them, severally,
his/her true and lawful attorney or attorneys-in-fact with or without the others
and with full power of substitution and resubstitution, to execute in his/her
name, place, and stead, in his/her capacity as a director or officer or both, as
the case may be, of the company, the Form 10-K and any and all amendments
thereto as said attorneys-in-fact or any of them shall deem necessary or
appropriate, together with all instruments necessary or incidental in connection
therewith, and to file the same or cause the same to be filed with the
Commission. Each of said attorneys-in-fact shall have full power and authority
to do and perform in the name and on behalf of the undersigned, in any and all
capacities, every act whatsoever necessary or desirable in connection with the
Form 10-K, as fully and for all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts of
said attorneys-in-fact and each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument this sixth
day of February, 1997.
 
                                              /s/ JAMES S. D'AGOSTINO, JR.
                                            ------------------------------------
                                                  James S. D'Agostino, Jr.
<PAGE>   4
 
                                                                      EXHIBIT 24
 
                AMERICAN GENERAL CORPORATION: BOARD OF DIRECTORS
 
Date:     February 6, 1997
Subject:  Form 10-K; Limited Power of Attorney for
 
Purpose.  The purpose of this limited power of attorney is to authorize certain
--------  officers of the company to execute, on behalf of the undersigned
          person, the company's 1996 annual report on Form 10-K, with such
          amendments thereto as may be necessary or appropriate, together with
          any and all exhibits and other related documents, and to file the 
          Form 10-K with the SEC.
 
                           LIMITED POWER OF ATTORNEY
 
     WHEREAS, AMERICAN GENERAL CORPORATION, a Texas corporation (company), will
file with the Securities and Exchange Commission (Commission) under Section 13
of the Securities Exchange Act of 1934, as amended (Act), its annual report on
Form 10-K for the fiscal year ended December 31, 1996 (Form 10-K), with such
amendments thereto as may be necessary or appropriate, together with any and all
exhibits and other documents related thereto;
 
     NOW, THEREFORE, the undersigned in his/her capacity as a director or
officer or both, as the case may be, of the company does hereby appoint JON P.
NEWTON, CARL J. SANTILLO, and JOHN A. ADKINS, and each of them, severally,
his/her true and lawful attorney or attorneys-in-fact with or without the others
and with full power of substitution and resubstitution, to execute in his/her
name, place, and stead, in his/her capacity as a director or officer or both, as
the case may be, of the company, the Form 10-K and any and all amendments
thereto as said attorneys-in-fact or any of them shall deem necessary or
appropriate, together with all instruments necessary or incidental in connection
therewith, and to file the same or cause the same to be filed with the
Commission. Each of said attorneys-in-fact shall have full power and authority
to do and perform in the name and on behalf of the undersigned, in any and all
capacities, every act whatsoever necessary or desirable in connection with the
Form 10-K, as fully and for all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts of
said attorneys-in-fact and each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument this sixth
day of February, 1997.
 
                                               /s/ W. LIPSCOMB DAVIS, JR.
                                            ------------------------------------
                                                   W. Lipscomb Davis, Jr.
<PAGE>   5
 
                                                                      EXHIBIT 24
 
                AMERICAN GENERAL CORPORATION: BOARD OF DIRECTORS
 
Date:     February 6, 1997
Subject:  Form 10-K; Limited Power of Attorney for
 
Purpose.  The purpose of this limited power of attorney is to authorize certain
--------  officers of the company to execute, on behalf of the undersigned
          person, the company's 1996 annual report on Form 10-K, with such
          amendments thereto as may be necessary or appropriate, together with
          any and all exhibits and other related documents, and to file the 
          Form 10-K with the SEC.
 
                           LIMITED POWER OF ATTORNEY
 
     WHEREAS, AMERICAN GENERAL CORPORATION, a Texas corporation (company), will
file with the Securities and Exchange Commission (Commission) under Section 13
of the Securities Exchange Act of 1934, as amended (Act), its annual report on
Form 10-K for the fiscal year ended December 31, 1996 (Form 10-K), with such
amendments thereto as may be necessary or appropriate, together with any and all
exhibits and other documents related thereto;
 
     NOW, THEREFORE, the undersigned in his/her capacity as a director or
officer or both, as the case may be, of the company does hereby appoint JON P.
NEWTON, CARL J. SANTILLO, and JOHN A. ADKINS, and each of them, severally,
his/her true and lawful attorney or attorneys-in-fact with or without the others
and with full power of substitution and resubstitution, to execute in his/her
name, place, and stead, in his/her capacity as a director or officer or both, as
the case may be, of the company, the Form 10-K and any and all amendments
thereto as said attorneys-in-fact or any of them shall deem necessary or
appropriate, together with all instruments necessary or incidental in connection
therewith, and to file the same or cause the same to be filed with the
Commission. Each of said attorneys-in-fact shall have full power and authority
to do and perform in the name and on behalf of the undersigned, in any and all
capacities, every act whatsoever necessary or desirable in connection with the
Form 10-K, as fully and for all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts of
said attorneys-in-fact and each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument this sixth
day of February, 1997.
 
                                                   /s/ HAROLD S. HOOK
                                            ------------------------------------
                                                       Harold S. Hook
<PAGE>   6
 
                                                                      EXHIBIT 24
 
                AMERICAN GENERAL CORPORATION: BOARD OF DIRECTORS
 
Date:     February 6, 1997
Subject:  Form 10-K; Limited Power of Attorney for
 
Purpose.  The purpose of this limited power of attorney is to authorize certain
--------  officers of the company to execute, on behalf of the undersigned
          person, the company's 1996 annual report on Form 10-K, with such
          amendments thereto as may be necessary or appropriate, together with
          any and all exhibits and other related documents, and to file the 
          Form 10-K with the SEC.
 
                           LIMITED POWER OF ATTORNEY
 
     WHEREAS, AMERICAN GENERAL CORPORATION, a Texas corporation (company), will
file with the Securities and Exchange Commission (Commission) under Section 13
of the Securities Exchange Act of 1934, as amended (Act), its annual report on
Form 10-K for the fiscal year ended December 31, 1996 (Form 10-K), with such
amendments thereto as may be necessary or appropriate, together with any and all
exhibits and other documents related thereto;
 
     NOW, THEREFORE, the undersigned in his/her capacity as a director or
officer or both, as the case may be, of the company does hereby appoint JON P.
NEWTON, CARL J. SANTILLO, and JOHN A. ADKINS, and each of them, severally,
his/her true and lawful attorney or attorneys-in-fact with or without the others
and with full power of substitution and resubstitution, to execute in his/her
name, place, and stead, in his/her capacity as a director or officer or both, as
the case may be, of the company, the Form 10-K and any and all amendments
thereto as said attorneys-in-fact or any of them shall deem necessary or
appropriate, together with all instruments necessary or incidental in connection
therewith, and to file the same or cause the same to be filed with the
Commission. Each of said attorneys-in-fact shall have full power and authority
to do and perform in the name and on behalf of the undersigned, in any and all
capacities, every act whatsoever necessary or desirable in connection with the
Form 10-K, as fully and for all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts of
said attorneys-in-fact and each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument this sixth
day of February, 1997.
 
                                                   /s/ LARRY D. HORNER
                                            ------------------------------------
                                                      Larry D. Horner
<PAGE>   7
 
                                                                      EXHIBIT 24
 
                AMERICAN GENERAL CORPORATION: BOARD OF DIRECTORS
 
Date:     February 6, 1997
Subject:  Form 10-K; Limited Power of Attorney for
 
Purpose.  The purpose of this limited power of attorney is to authorize certain
--------  officers of the company to execute, on behalf of the undersigned
          person, the company's 1996 annual report on Form 10-K, with such
          amendments thereto as may be necessary or appropriate, together with
          any and all exhibits and other related documents, and to file the 
          Form 10-K with the SEC.
 
                           LIMITED POWER OF ATTORNEY
 
     WHEREAS, AMERICAN GENERAL CORPORATION, a Texas corporation (company), will
file with the Securities and Exchange Commission (Commission) under Section 13
of the Securities Exchange Act of 1934, as amended (Act), its annual report on
Form 10-K for the fiscal year ended December 31, 1996 (Form 10-K), with such
amendments thereto as may be necessary or appropriate, together with any and all
exhibits and other documents related thereto;
 
     NOW, THEREFORE, the undersigned in his/her capacity as a director or
officer or both, as the case may be, of the company does hereby appoint JON P.
NEWTON, CARL J. SANTILLO, and JOHN A. ADKINS, and each of them, severally,
his/her true and lawful attorney or attorneys-in-fact with or without the others
and with full power of substitution and resubstitution, to execute in his/her
name, place, and stead, in his/her capacity as a director or officer or both, as
the case may be, of the company, the Form 10-K and any and all amendments
thereto as said attorneys-in-fact or any of them shall deem necessary or
appropriate, together with all instruments necessary or incidental in connection
therewith, and to file the same or cause the same to be filed with the
Commission. Each of said attorneys-in-fact shall have full power and authority
to do and perform in the name and on behalf of the undersigned, in any and all
capacities, every act whatsoever necessary or desirable in connection with the
Form 10-K, as fully and for all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts of
said attorneys-in-fact and each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument this sixth
day of February, 1997.
 
                                                /s/ RICHARD J.V. JOHNSON
                                            ------------------------------------
                                                    Richard J.V. Johnson
<PAGE>   8
 
                                                                      EXHIBIT 24
 
                AMERICAN GENERAL CORPORATION: BOARD OF DIRECTORS
 
Date:     February 6, 1997
Subject:  Form 10-K; Limited Power of Attorney for
 
Purpose.  The purpose of this limited power of attorney is to authorize certain
--------  officers of the company to execute, on behalf of the undersigned
          person, the company's 1996 annual report on Form 10-K, with such
          amendments thereto as may be necessary or appropriate, together with
          any and all exhibits and other related documents, and to file the 
          Form 10-K with the SEC.
 
                           LIMITED POWER OF ATTORNEY
 
     WHEREAS, AMERICAN GENERAL CORPORATION, a Texas corporation (company), will
file with the Securities and Exchange Commission (Commission) under Section 13
of the Securities Exchange Act of 1934, as amended (Act), its annual report on
Form 10-K for the fiscal year ended December 31, 1996 (Form 10-K), with such
amendments thereto as may be necessary or appropriate, together with any and all
exhibits and other documents related thereto;
 
     NOW, THEREFORE, the undersigned in his/her capacity as a director or
officer or both, as the case may be, of the company does hereby appoint JON P.
NEWTON, CARL J. SANTILLO, and JOHN A. ADKINS, and each of them, severally,
his/her true and lawful attorney or attorneys-in-fact with or without the others
and with full power of substitution and resubstitution, to execute in his/her
name, place, and stead, in his/her capacity as a director or officer or both, as
the case may be, of the company, the Form 10-K and any and all amendments
thereto as said attorneys-in-fact or any of them shall deem necessary or
appropriate, together with all instruments necessary or incidental in connection
therewith, and to file the same or cause the same to be filed with the
Commission. Each of said attorneys-in-fact shall have full power and authority
to do and perform in the name and on behalf of the undersigned, in any and all
capacities, every act whatsoever necessary or desirable in connection with the
Form 10-K, as fully and for all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts of
said attorneys-in-fact and each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument this sixth
day of February, 1997.
 
                                                 /s/ ROBERT E. SMITTCAMP
                                            ------------------------------------
                                                    Robert E. Smittcamp
<PAGE>   9
 
                                                                      EXHIBIT 24
 
                AMERICAN GENERAL CORPORATION: BOARD OF DIRECTORS
 
Date:     February 6, 1997
Subject:  Form 10-K; Limited Power of Attorney for
 
Purpose.  The purpose of this limited power of attorney is to authorize certain
--------  officers of the company to execute, on behalf of the undersigned
          person, the company's 1996 annual report on Form 10-K, with such
          amendments thereto as may be necessary or appropriate, together with
          any and all exhibits and other related documents, and to file the 
          Form 10-K with the SEC.
 
                           LIMITED POWER OF ATTORNEY
 
     WHEREAS, AMERICAN GENERAL CORPORATION, a Texas corporation (company), will
file with the Securities and Exchange Commission (Commission) under Section 13
of the Securities Exchange Act of 1934, as amended (Act), its annual report on
Form 10-K for the fiscal year ended December 31, 1996 (Form 10-K), with such
amendments thereto as may be necessary or appropriate, together with any and all
exhibits and other documents related thereto;
 
     NOW, THEREFORE, the undersigned in his/her capacity as a director or
officer or both, as the case may be, of the company does hereby appoint JON P.
NEWTON, CARL J. SANTILLO, and JOHN A. ADKINS, and each of them, severally,
his/her true and lawful attorney or attorneys-in-fact with or without the others
and with full power of substitution and resubstitution, to execute in his/her
name, place, and stead, in his/her capacity as a director or officer or both, as
the case may be, of the company, the Form 10-K and any and all amendments
thereto as said attorneys-in-fact or any of them shall deem necessary or
appropriate, together with all instruments necessary or incidental in connection
therewith, and to file the same or cause the same to be filed with the
Commission. Each of said attorneys-in-fact shall have full power and authority
to do and perform in the name and on behalf of the undersigned, in any and all
capacities, every act whatsoever necessary or desirable in connection with the
Form 10-K, as fully and for all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts of
said attorneys-in-fact and each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument this sixth
day of February, 1997.
 
                                                   /s/ ANNE M. TATLOCK
                                            ------------------------------------
                                                      Anne M. Tatlock