<PAGE>
                                                                    EXHIBIT 4(b)


      AGREEMENT OF RESIGNATION, APPOINTMENT AND ACCEPTANCE, dated as of July 25,
2006 by and among AMERICAN GENERAL FINANCE CORPORATION, a corporation duly
organized and existing under the laws of State of Indiana and having its
principal office at 601 N.W. Second Street, Evansville, Indiana 47708 (the
"Company"), WILMINGTON TRUST COMPANY a BANKING CORPORATION duly organized and
existing under the laws of the STATE OF DELAWARE and having its principal
corporate trust office at Rodney Square North, 1100 North Market Street,
Wilmington, Delaware 19890 ("Successor Trustee") and CITIBANK, N.A., a national
banking association duly organized and existing under the laws of the United
States of America having its principal corporate trust office at 388 Greenwich
Street, 14th Floor, New York, New York 10013 ("Resigning Trustee"). Capitalized
terms not otherwise defined herein shall have the meanings given to them in the
Indenture (as defined below).

                                    RECITALS:

      WHEREAS, there are currently $14,007,980,000.00 aggregate principal amount
of the Company's Senior Debt Securities (the "Securities") outstanding under the
Indenture dated as of May 1, 1999, by and between the Company and the Resigning
Trustee (the "Indenture");

      WHEREAS, the Company appointed the Resigning Trustee as the Trustee,
Security Registrar and Paying Agent under the Indenture.

      WHEREAS, Section 610 of the Indenture provides that the Trustee may at any
time resign with respect to the Securities of one or more series by giving
written notice of such resignation to the Company, effective upon the acceptance
by a successor Trustee of its appointment as a successor Trustee;

      WHEREAS, Section 610(e) of the Indenture provides that, if the Trustee
shall resign, the Company, by or pursuant to a Board Resolution, shall promptly
appoint a successor Trustee;

      WHEREAS, Section 611(a) of the Indenture provides that any successor
Trustee appointed in accordance with the Indenture shall execute, acknowledge
and deliver to the Company and to the retiring trustee an instrument accepting
such appointment under the

<PAGE>

Indenture, and thereupon the resignation of the retiring Trustee shall become
effective and such successor Trustee, without any further act, deed or
conveyance, shall become vested with all rights, powers, trusts and duties of
the retiring trustee;

      WHEREAS, the Company desires to appoint Successor Trustee as Trustee to
succeed Resigning Trustee in such capacity under the Indenture; and

      WHEREAS, Successor Trustee is willing to accept such appointment as
successor Trustee, under the Indenture;

      NOW, THEREFORE, the Company, Resigning Trustee and Successor Trustee, for
and in consideration of the premises and of other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged,
hereby consent and agree as follows:

                                       1

                              THE RESIGNING TRUSTEE

      1.1 Pursuant to Section 610(b) of the Indenture, Resigning Trustee hereby
notifies the Company that Resigning Trustee is hereby resigning as Trustee under
the Indenture, but (a) will retain the roles of Security Registrar and Paying
Agent under the Indenture and (b) accepts its appointment set forth in Article 3
hereof, as Authenticating Agent with respect to all Securities issued or to be
issued under the Indenture.

      1.2 Resigning Trustee hereby represents and warrants to Successor Trustee
that:

      (a) No covenant or condition contained in the Indenture has been waived by
Resigning Trustee or, to the best knowledge of responsible officers of Resigning
Trustee's corporate trust department, by the Holders of the percentage in
aggregate principal amount of the Securities required by the Indenture to effect
any such waiver.

      (b) There is no action, suit or proceeding pending or, to the best
knowledge of responsible officers of Resigning Trustee's corporate trust
department, threatened against Resigning Trustee before any court or any
governmental authority arising out of any act or omission of Resigning Trustee
as Trustee under the Indenture.

      (c) As of the effective date of this Agreement, Resigning Trustee will
hold no moneys or property under the Indenture.


                                      -2-
<PAGE>

      (d) Pursuant to Section 303 of the Indenture, Resigning Trustee has duly
authenticated and delivered, $14,007,980,000.00 aggregate principal amount of
Securities which remain outstanding as of the effective date hereof.

      (e) The registers in which the Resigning Trustee has registered and
transferred registered Securities accurately reflect the amount of Securities
issued and outstanding and the amounts payable thereon.

      (f) Each person who so authenticated the Securities was duly elected,
qualified and acting as an officer of Resigning Trustee and empowered to
authenticate the Securities at the respective times of such authentication and
the signature of such person or persons appearing on such Securities is each
such person's genuine signature.

      (g) This Agreement has been duly authorized, executed and delivered on
behalf of Resigning Trustee and constitutes its legal, valid and binding
obligation, enforceable in accordance with its terms.

      (h) To the best knowledge of responsible officers of the Resigning
Trustee's corporate trust department, no event has occurred and is continuing
which is, or after notice or lapse of time would become, an Event of Default
under Section 501 of the Indenture.

      1.3 Resigning Trustee hereby represents and warrants to Successor Trustee
and the Company that its satisfies the Authenticating Agent eligibility
requirements of Section 613 of the Indenture.

      1.4 Resigning Trustee hereby assigns, transfers, delivers and confirms to
Successor Trustee all right, title and interest of Resigning Trustee in and to
the trust under the Indenture and all the rights, powers and trusts of the
Resigning Trustee under the Indenture. Resigning Trustee shall execute and
deliver such further instruments and shall do such other things as Successor
Trustee may reasonably require so as to more fully and certainly vest and
confirm in Successor Trustee all the rights, powers and trusts hereby assigned,
transferred, delivered and confirmed to Successor Trustee as Trustee.

      1.5 Resigning Trustee shall deliver to Successor Trustee, as of or
immediately after the effective date hereof, all of the documents listed on
Exhibit A hereto.


                                      -3-
<PAGE>

                                       2

                                   THE COMPANY

      2.1 The Company hereby (a) accepts the resignation of Resigning Trustee as
Trustee under the Indenture (b) approves the appointment of the Resigning
Trustee as Authenticating Agent with respect to all Securities issued under the
Indenture and (c) acknowledges that the Resigning Trustee will retain the roles
of Security Registrar and Paying Agent under the Indenture.

      2.2 The Company hereby certifies that Exhibit B annexed hereto are true
copies of resolutions duly adopted by the Terms and Pricing Committee of the
Company's Board of Directors, which resolution remain in full force and effect
on the date hereof, and which authorizes, among other things, certain officers
of the Company to: (a) accept Resigning Trustee's resignation as Trustee under
the Indenture; (b) appoint Successor Trustee as Trustee under the Indenture; and
(c) execute and deliver such agreements and other instruments as may be
necessary or desirable to effectuate the succession of Successor Trustee as
Trustee under the Indenture.

      2.3 The Company hereby appoints Successor Trustee as Trustee under the
Indenture to succeed to, and hereby vests Successor Trustee with, all the
rights, powers, duties and obligations of Resigning Trustee under the Indenture
with like effect as if originally named as Trustee in the Indenture.

      2.4 Promptly after the effective date of this Agreement, the Company shall
cause a notice, substantially in the form of Exhibit C annexed hereto, to be
sent to each Holder of the Securities in accordance with the provisions of
Section 106 of the Indenture.

      2.5 The Company hereby represents and warrants to Resigning Trustee and
Successor Trustee that:

            (a)   The Company is a corporation duly and validly organized and
                  existing pursuant to the laws of the State of Indiana.

            (b)   The Indenture was validly and lawfully executed and delivered
                  by the Company and the Securities were validly issued by the
                  Company.


                                      -4-
<PAGE>

            (c)   To the best of its knowledge, the Company has performed or
                  fulfilled prior to the date hereof, and will continue to
                  perform and fulfill after the date hereof, each covenant,
                  agreement, condition, obligation and responsibility under the
                  Indenture.

            (d)   No event has occurred and is continuing which is, or after
                  notice or lapse of time would become, an Event of Default
                  under Section 501 of the Indenture.

            (e)   To the best of its knowledge, no covenant or condition
                  contained in the Indenture has been waived by the Company or,
                  to the best of the Company's knowledge, by Holders of the
                  percentage in aggregate principal amount of the Securities
                  required to effect any such waiver.

            (f)   To the best of its knowledge, there is no action, suit or
                  proceeding pending or, to the best of the Company's knowledge,
                  threatened against the Company before any court or any
                  governmental authority arising out of any act or omission of
                  the Company under the Indenture.

            (g)   This Agreement has been duly authorized, executed and
                  delivered on behalf of the Company and constitutes its legal,
                  valid and binding obligation, enforceable in accordance with
                  its terms.

            (h)   All conditions precedent relating to the appointment of
                  Wilmington Trust Company as successor Trustee under the
                  Indenture have been complied with by the Company.

                                       3

                              THE SUCCESSOR TRUSTEE

      3.1 Successor Trustee hereby represents and warrants to Resigning Trustee
and to the Company that:

            (a)   Successor Trustee is not disqualified under the provisions of
                  Section 608 and is eligible under the provisions of Section
                  609 of the Indenture to act as Trustee under the Indenture.


                                      -5-
<PAGE>

            (b)   This Agreement has been duly authorized, executed and
                  delivered on behalf of Successor Trustee and constitutes its
                  legal, valid and binding obligation, enforceable in accordance
                  with its terms.

      3.2 Successor Trustee hereby accepts its appointment as successor Trustee
under the Indenture and accepts the rights, powers, duties and obligations of
Resigning Trustee as Trustee under the Indenture, upon the terms and conditions
set forth therein, with like effect as if originally named as Trustee under the
Indenture.

      3.3 References in the Indenture to "Corporate Trust Office" or other
similar terms shall be deemed to refer to the principal corporate trust office
of Successor Trustee, which is presently located at Rodney Square North, 1100
North Market Street, Wilmington, Delaware 19890.

      3.4 Successor Trustee hereby appoints, pursuant to Section 613 of the
Indenture, Resigning Trustee as Authenticating Agent with respect to all
Securities issued or to be issued under the Indenture.

                                       4

                                  MISCELLANEOUS

      4.1 Except as otherwise expressly provided herein or unless the context
otherwise requires, all terms used herein which are defined in the Indenture
shall have the meanings assigned to them in the Indenture.

      4.2 This Agreement and the resignation, appointments, approval and
acceptance effected hereby shall be effective as of the opening of business on
July 26, 2006.

      4.3 Resigning Trustee hereby acknowledges payment or provision for payment
in full by the Company of compensation for all services rendered by Resigning
Trustee in its capacity as Trustee under Section 607 of the Indenture and
reimbursement in full by the Company of the expenses, disbursements and advances
incurred or made by Resigning Trustee in its capacity as Trustee in accordance
with the provisions of the Indenture. Resigning Trustee acknowledges that it
relinquishes any lien it may have upon all property or funds held or collected
by it to secure any amounts due. The Company acknowledges that the provisions of
Section 607 of the Indenture remain in effect.


                                      -6-
<PAGE>

      4.4 This Agreement shall be governed by and construed in accordance with
the laws of the State of New York.

      4.5 This Agreement may be executed in any number of counterparts each of
which shall be an original, but such counterparts shall together constitute but
one and the same instrument.

      4.6 The Company, Resigning Trustee and Successor Trustee hereby
acknowledge receipt of an executed and acknowledged counterpart of this
Agreement and the effectiveness thereof.

      IN WITNESS WHEREOF, the parties hereto have caused this Agreement of
Resignation, Appointment and Acceptance to be duly executed and acknowledged and
duly attested all as of the day and year first above written.

[SEAL]                                   AMERICAN GENERAL FINANCE CORPORATION

Attest:                                  By: /s/ Bryan A. Binyon
                                            -----------------------------------
                                            Name:  Bryan A. Binyon
                                            Title: Vice President and Treasurer
/s/ Linda C. Meredith
------------------------------
Name:  Linda C. Meredith
Title: Assistant Secretary


[SEAL]

Attest:                                  CITIBANK, N.A.
                                         as Resigning Trustee

                                         By: /s/ Jennifer McCourt
                                            -----------------------------------
                                            Name:  Jennifer McCourt
                                            Title:

/s/ Karen Schluter
------------------------------
Name:  Karen Schluter
Title:


                                      -7-
<PAGE>

[SEAL]

Attest:                              WILMINGTON TRUST COMPANY, as
                                     Successor Trustee

                                     By: /s/ Kristin L. Moore
                                        --------------------------------
                                        Name:  Kristin L. Moore
                                        Title: Senior Financial Services Officer

/s/ Mary C. St. Amand
------------------------------
Name:  Mary C. St. Amand
Title: Assistant Vice President


                                      -8-
<PAGE>

                                    EXHIBIT A

                 Documents to be delivered to Successor Trustee

1.    Executed copy of the Indenture.

2.    Conformed copy of Indenture.

3.    File of closing documents from initial issuance.

4.    Copies of the most recent of each of the SEC reports delivered by the
      Company pursuant to Section 704 of the Indenture.

5.    A copy of the most recent compliance certificate delivered pursuant to
      Section 1005 of the Indenture.

6.    Certified list of Holders, including certificate detail and all "stop
      transfers" and the reason for such "stop transfers" (or, alternatively, if
      there are a substantial number of registered Holders, the computer tape
      reflecting the identity of such Holders).

7.    Copies of any official notices sent by the Trustee to all the Holders of
      the Securities pursuant to the terms of the Indenture during the past
      twelve months and a copy of the most recent Trustee's annual report to
      holders delivered pursuant to Section 703 of the Indenture.

8.    List of any documents which, to the knowledge of Resigning Trustee, are
      required to be furnished but have not been furnished to Resigning Trustee,
      or if none, a statement from the Resigning Trustee to that effect.

<PAGE>

                                    EXHIBIT B

            Trustee Resignation; Successor Trustee Appointment.

            FURTHER RESOLVED, that the resignation of Citibank, N.A. as Trustee
under the Indenture dated as of May 1, 1999 between the Company and Citibank,
N.A., as Trustee (the "Indenture" and Citibank, N.A., in its capacity as
resigning Trustee, the "Resigning Trustee"), is hereby accepted, such
resignation to be effective upon the execution, delivery and effectiveness of an
instrument or instruments pursuant to which Wilmington Trust Company ("Successor
Trustee") accepts appointment as successor Trustee under the Indenture (such
instrument or instruments collectively being referred to herein as the
"Agreement of Resignation, Appointment and Acceptance"); and be it

            FURTHER RESOLVED, that the Successor Trustee be, and it hereby is,
designated and appointed as successor Trustee under the Indenture; and be it

            FURTHER RESOLVED, that the form of Agreement of Resignation,
Appointment and Acceptance presented to this Committee and attached hereto, and
the terms and conditions set forth therein, are hereby approved; and that the
Chairman, the Chief Executive Officer, the President or the Treasurer be, and
each of them hereby is, authorized and empowered to make or cause to be made
such further changes in the form of Agreement of Resignation, Appointment and
Acceptance as they may deem necessary or desirable; and be it

            FURTHER RESOLVED, that the Chairman, the Chief Executive Officer,
the President, the Chief Financial Officer, the Treasurer, any Assistant
Treasurer, the Secretary or any Assistant Secretary of the Company (the
"Authorized Officers") be, and each of them hereby is, authorized and empowered
in the name and on behalf of the Company to do or cause to be done all such acts
or things, and to execute and deliver, or cause to be executed or delivered, any
and all such other agreements, amendments, instruments, certificates, documents
or papers (including, without limitation, any and all notices and certificates
required or permitted to be given or made on behalf of the Company to the
Successor Trustee or to the Resigning Trustee), under the terms of any of the
executed instruments in connection with the resignation of Resigning Trustee and
the appointment of Successor Trustee in the name and on behalf of the Company as
any of such officers, in his or her discretion, may deem necessary or advisable
to effectuate or carry out the purposes and intent of the foregoing resolutions;
and to perform any of the Company's obligations under the instruments and
agreements executed on behalf of the Company in connection with the resignation
of the Resigning Trustee and the appointment of the Successor Trustee.

            c.    Indenture Authorization.

            FURTHER RESOLVED, that the Debt Securities shall be issued under the
Indenture; and that the Chairman, the Chief Executive Officer, the President or
the Treasurer be, and each of them hereby is, authorized and empowered to take
any such


<PAGE>

action as may be necessary or appropriate to qualify the Indenture under the
Trust Indenture Act of 1939, as amended, for purposes of the Registration
Statement; and be it

            Paying Agent and Security Registrar.

FURTHER RESOLVED, that Citibank, N.A. be, and it hereby is, designated and
appointed as the Paying Agent, Security Registrar and Authenticating Agent with
respect to the Debt Securities;

<PAGE>

                                    EXHIBIT C
                              [COMPANY LETTERHEAD]
                                     NOTICE

To the Holders of:

[List Indentures and relevant Cusips]



            NOTICE IS HEREBY GIVEN, pursuant to Section 106 of the Indenture
(the "Indenture") dated as of May 1, 1999 by and between American General
Finance (the "Company") and Citibank, N.A., as Trustee, that Citibank, N.A. has
resigned as Trustee under the Indenture, but will serve as Authenticating Agent,
Security Registrar and Paying Agent under the Indenture.

            Pursuant to Sections 611 of the Indenture, Wilmington Trust Company,
a banking corporation duly organized and existing under the laws of the State of
Delaware, has accepted appointment as Trustee under the Indenture. The address
of the corporate trust office of Wilmington Trust Company is Rodney Square
North, 1100 North Market Street, Wilmington, Delaware 19890

            Citibank's resignation as Trustee and Wilmington Trust Company's
appointment as successor Trustee were effective as of the opening of business on
July 26, 2006.

                                       AMERICAN GENERAL FINANCE CORPORATION

                                       By:
                                           ----------------------------
                                           Name:
                                           Title:




Dated:  New York, New York
        July ___, 2006