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                                                                    EXHIBIT 4(k)

                          AMERICAN GENERAL CORPORATION


                RESOLUTIONS RELATING TO 6% SERIES A CONVERTIBLE
                    JUNIOR SUBORDINATED DEBENTURES DUE 2025
                         ADOPTED BY THE TERMS COMMITTEE

          WHEREAS, American General Delaware, L.L.C., a Delaware limited
liability company ("American General Delaware"), proposes to issue its 6%
Convertible Monthly Income Preferred Securities, Series A (collectively, the
"Series A Preferred Securities") and use the proceeds from the sale of such
Preferred Securities to purchase junior subordinated debentures of the Company;
and

          WHEREAS, this Committee desires to establish the terms of such junior
subordinated debentures pursuant to Section 301 of the Indenture, dated as of
May 15, 1995 (the "Indenture"), between the Company and Chemical Bank, as
Trustee;

          Now, therefore, be it:

          RESOLVED, that, upon receipt of the purchase price therefor, the
Company shall issue, sell and deliver a series of its junior subordinated
debentures pursuant to the Indenture.

          RESOLVED, that the title, principal amount, interest rate, redemption
provisions, conversion and exchange features, and other terms of such debentures
to be fixed pursuant to Section 301 of the Indenture shall be as follows
(capitalized terms appearing below that are defined in the Indenture, but not
defined herein, having the meanings ascribed to them in the Indenture):

          1.  TITLE.  Each of such debentures shall be designated as "6% Series
A Convertible Junior Subordinated Debenture due 2025" (collectively, the "Series
A Junior Subordinated Debentures") and each such Series A Junior Subordinated
Debenture shall be included in the series of Securities so designated.

          2.  PRINCIPAL AMOUNT.  The aggregate principal amount of the Series A
Junior Subordinated Debentures which may be authenticated and delivered pursuant
to these resolutions shall be limited to $281,962,050 or, if and to the extent
that the underwriters underwriting the sale of the Series A Preferred Securities
exercise their overallotment option with respect thereto, then such aggregate
principal amount of Series A Junior Subordinated Debentures shall be up to
$313,291,100 (except, in each case, for Series A Junior Subordinated Debentures
authenticated and delivered upon registration of transfer of, or in exchange
for, or in lieu of, other Series A Junior Subordinated Debentures pursuant to
Section 304, 305, 306, 907 or 1107 of the Indenture).

          3.  MATURITY DATE.  The principal of the Series A Junior Subordinated
Debentures shall be payable (together with any accrued and unpaid interest
thereon, including

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Additional Interest, as defined in Section 6, if any) on the earlier of (a) May
31, 2025, or (b) the date upon which American General Delaware is liquidated,
dissolved or wound-up; provided, however, that, if all the Series A Preferred
Securities are exchanged for Series A Junior Subordinated Debentures (a "Series
A Special Event Exchange") in the manner set forth in Section 5(d) of the
Written Action, dated as of May 24, 1995 (the "Written Action"), of the Managing
Member of American General Delaware establishing the Series A Preferred
Securities, the Series A Junior Subordinated Debentures will mature on the date
set forth in clause (a), notwithstanding that American General Delaware may have
liquidated, dissolved or wound-up in connection with or after such Series A
Special Event Exchange.

          4.  INTEREST RATE; INTEREST PAYMENT DATES.  The Series A Junior
Subordinated Debentures shall bear interest at the rate of 6% per annum;
interest shall accrue from June 1, 1995 or from the most recent Interest Payment
Date to which interest has been paid or duly provided for; the Interest Payment
Dates on which such interest shall be payable shall be the last day of each
calendar month of each year, commencing June 30, 1995, until the principal is
paid in full or such payment is duly provided for; and the Regular Record Date
for the interest payable upon any such Interest Payment Date shall be the
Business Day next preceding such Interest Payment Date; provided, however, that
if the Series A Junior Subordinated Debentures are not in book-entry-only form
during any period following a Series A Special Event Exchange, the Regular
Record Date for any Interest Payment Date within such period shall be the
fifteenth day of the month in which such Interest Payment Date occurs.  If any
date on which interest is payable on the Series A Junior Subordinated Debentures
is not a Business Day, then the payment of the interest payable on such date
will be made on the next succeeding day which is a Business Day (and without any
interest or other payment in respect of any such delay), except that, if such
Business Day is in the next succeeding calendar year, such payment shall be made
on the immediately preceding Business Day, in each case with the same force and
effect as if made on such date.

          5.  EXTENSION OF AN INTEREST PAYMENT PERIOD.  The Company shall have
the right, at any time and from time to time during the term of the Series A
Junior Subordinated Debentures, to extend the interest payment period to a
period ending on the last day of a calendar month (an "Extension Period") not
exceeding 60 consecutive months, but in no event beyond the date of Stated
Maturity or the Redemption Date of the Series A Junior Subordinated Debentures.
During an Extension Period, interest will continue to accrue and compound
monthly in the manner set forth in Section 6 below.  Prior to the termination of
any Extension Period of less than 60 consecutive months, the Company may further
extend the interest payment period, provided that such Extension Period may not
exceed 60 consecutive months and may not extend beyond the date of Stated
Maturity or the Redemption Date of the Series A Junior Subordinated Debentures.
Upon the termination of any Extension Period and the payment of all accrued and
unpaid interest (including Additional Interest) then due, the Company may select
a new Extension Period, subject to the above requirements.  No interest shall be
due during an Extension Period until the end of such period.  Such interest
shall be due and payable on the Interest Payment Date which is the last day of
the Extension Period.  The Regular Record Date for the interest payable

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on such Interest Payment Date shall be the Business Day next preceding such
Interest Payment Date, provided that if the Series A Junior Subordinated
Debentures are not in book-entry-only form during any period following a Series
A Special Event Exchange, the Regular Record Date for such payment shall be the
15th day of the month in which such Interest Payment Date occurs.

          At any time prior to a Series A Special Event Exchange and if any
Series A Preferred Securities are then outstanding, the Company shall give
American General Delaware notice of its selection of an Extension Period at
least one Business Day prior to the earlier of (i) the date that dividends on
the Series A Preferred Securities are payable or (ii) the date on which American
General Delaware is required to give notice of the record or payment date of any
dividend payable on the Series A Preferred Securities to the New York Stock
Exchange ("NYSE") or other applicable self-regulatory organization or to holders
of the Series A Preferred Securities, but in any event not less than one
Business Day prior to such record date.  After any Series A Special Event
Exchange, the Company shall give the holders of the Series A Junior Subordinated
Debentures notice of its selection of an Extension Period not less than two
Business Days prior to the Regular Record Date for the first Interest Payment
Date for which such Extension Period will be effective.  In each case, the
Company shall give the Trustee notice of its selection of an Extension Period
not later than the Business Day such notice is required to be given to American
General Delaware or the Holders of the Series A Junior Subordinated Debentures,
as the case may be, pursuant to the preceding provisions of this paragraph.

          Notice of the Company's extension of an Extension Period shall be
given prior to the then scheduled end of the Extension Period in a manner
similar to the notice given in connection with the selection of an Extension
Period.

          6.  ADDITIONAL INTEREST.  Interest shall accrue at the rate of 6% per
annum on any interest on the Series A Junior Subordinated Debentures that is not
paid during an Extension Period.  Such interest shall compound monthly.  The
Company shall pay such interest, to the fullest extent permitted by applicable
law, on the Interest Payment Date which is the last day of the Extension Period.
Additionally, if at any time prior to a Series A Special Event Exchange,
American General Delaware shall be required to pay, with respect to the income
it derives from the interest payments on the Series A Junior Subordinated
Debentures, any amounts for or on account of any taxes, duties, assessments or
governmental charges of whatever nature imposed by the United States (other than
withholding taxes), or any other taxing authority, then, in any such case, the
Company shall pay, to the fullest extent permitted by applicable law, as
additional interest such additional amounts (the "Additional Amounts") as may be
necessary in order that the net amounts received and retained by American
General Delaware with respect to interest payments on the Series A Junior
Subordinated Debentures, after the payment of such taxes, duties, assessments or
governmental charges (including such taxes, duties, assessments or governmental
charges payable with respect to Additional Amounts), shall result in American
General Delaware's having such funds as it would have had in the absence of the
payment of such taxes, duties, assessments or governmental charges.  Such
Additional Amounts shall be payable when the related interest payment on the
Series A Junior Subordinated

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Debentures is due, except that, if the existence or applicability of such taxes,
duties, assessments or governmental charges is not known by the Company at the
time of such interest payment, then on the Interest Payment Date immediately
preceding the date on which American General Delaware proposes to pay such
taxes, duties, assessments or charges.  The amounts of interest payable to
effect monthly compounding on the Series A Junior Subordinated Debentures
pursuant to the first three sentences of this Section 6, together with any such
Additional Amounts, are referred to herein as "Additional Interest."

          In addition to the Additional Interest, the Company shall be required
to pay interest, at the rate borne by the Series A Junior Subordinated
Debentures, on any principal or premium that is not paid when due and, to the
extent that payment of such interest is lawful, interest on overdue installments
of interest (which shall not include interest not paid because of an extension
of an interest payment period).

          7.  PLACE OF PAYMENT.  The Trustee is hereby appointed as the initial
sole Paying Agent for the Series A Junior Subordinated Debentures.  The
principal of and interest (including any Additional Interest) on the Series A
Junior Subordinated Debentures shall be payable at the Corporate Trust Office of
the Trustee in the Borough of Manhattan, The City of New York, provided,
however, that, at the option of the Company, payment of interest may be made (a)
by check mailed to the address of the Person entitled thereto as such address
shall appear in the Security Register or (b) subject to the procedures of the
Paying Agent, by wire transfer in immediately available funds at such place and
to such account maintained at a bank located in the United States as may be
designated by the Person entitled thereto as specified in the Security Register.

          8.  CONDITIONAL RIGHT OF REDEMPTION.  If at any time following the
Conversion Expiration Date or the Conversion Expiration Date of the Series A
Junior Subordinated Debentures (as such terms are defined in Section 12(d)),
less than 10% of the aggregate principal amount of the Series A Junior
Subordinated Debentures originally purchased by American General Delaware with
the proceeds from the sale of the Series A Preferred Securities remains
Outstanding, then the Series A Junior Subordinated Debentures shall be subject
to redemption, in whole but not in part, at the option of the Company, at a
Redemption Price equal to the unpaid principal amount thereof, without premium
or penalty, plus any accrued and unpaid interest (including any Additional
Interest) thereon to the Redemption Date.

          9.  MANDATORY REDEMPTION.

          (a) If, prior to a Series A Special Event Exchange, American General
Delaware redeems any Series A Preferred Securities in accordance with the terms
thereof, then the Series A Junior Subordinated Debentures shall be due and
payable and shall be redeemed by the Company in an aggregate principal amount
equal to the aggregate stated liquidation preference of the Series A Preferred
Securities so redeemed at a cash Redemption Price equal to the unpaid principal
amount of the Series A Junior Subordinated Debentures so redeemed, without
premium or penalty, plus any accrued and unpaid interest (including any
Additional Interest) thereon to the Redemption Date.  Any redemption pursuant to
this

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Section shall be made prior to 12:00 noon, New York time, on the date of such
redemption of the Series A Preferred Securities (or at such other time on such
earlier date as the Company and American General Delaware shall agree).

          (b) In the case of a redemption pursuant to this Section 9, the
Company shall, at least one Business Day prior to the Redemption Date, notify
the Trustee of such Redemption Date and of the principal amount of the Series A
Junior Subordinated Debentures to be redeemed.  If the related redemption of
Series A Preferred Securities does not occur, then such redemption of the Series
A Junior Subordinated Debentures shall be of no force and effect,
notwithstanding the giving of such notice of redemption.

          10.  OPTIONAL REDEMPTION.  The Series A Junior Subordinated Debentures
shall be subject to redemption, at the option of the Company, in whole or in
part, at any time or from time to time on or after May 31, 2003 at a cash
Redemption Price equal to the unpaid principal amount thereof, without premium
or penalty, plus any accrued and unpaid interest (including any Additional
Interest) thereon to the Redemption Date.

          Additionally, if, prior to a Series A Special Event Exchange, the
Company or any of its Subsidiaries acquires any Series A Preferred Securities by
tender, in the open market, or otherwise, the Company shall have the right to
redeem the Series A Junior Subordinated Debentures in a principal amount not to
exceed the aggregate stated liquidation preference of the Series A Preferred
Securities so purchased, at a cash Redemption Price equal to the unpaid
principal amount thereof, without premium or penalty, plus any accrued and
unpaid interest (including any Additional Interest) thereon to the Redemption
Date.

          11. CONVERSION INTO AMERICAN GENERAL COMMON STOCK.

          (a) Conversion Price.  The Series A Junior Subordinated Debentures
shall be convertible, at the option of the Holders, at any time on or before the
earlier of the Conversion Expiration Date or the Conversion Expiration Date of
the Series A Junior Subordinated Debentures, into fully paid and nonassessable
shares of American General Common Stock at an initial conversion price of $40.69
principal amount of Series A Junior Subordinated Debentures per share of
American General Common Stock, subject to adjustment as described in Section 13
(such conversion price, as so adjusted, being herein called the "Conversion
Price").  Subject to the provisions of this Section 11 and Section 12, a Holder
of Series A Junior Subordinated Debentures may convert any portion of the
principal amount of the Series A Junior Subordinated Debentures held by it into
that number of fully paid and nonassessable full shares of American General
Common Stock obtained by dividing the aggregate principal amount of the Series A
Junior Subordinated Debentures to be converted by such Holder by such Conversion
Price.

          (b) Conversion Procedure Prior to Series A Special Event Exchange.
The Written Action provides that a holder of Series A Preferred Securities
wishing to exercise its right under such Written Action to convert Series A
Preferred Securities into American General Common Stock shall surrender to the
Conversion Agent, as defined in Section 16, such Series A Preferred Securities
(or, if such Series A Preferred Securities are in book-entry

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form, cause such Series A Preferred Securities to be transferred to the account
of the Conversion Agent on the records of the Depository), together with an
irrevocable notice of conversion setting forth the number of Series A Preferred
Securities to be converted, together with the name or names, if other than the
holder, in which the shares of American General Common Stock to be issued upon
conversion are to be registered and directing it (i) to exchange such Series A
Preferred Securities for the appropriate portion of the Series A Junior
Subordinated Debentures held by American General Delaware at the exchange rate
specified in the Written Action and (ii) to immediately convert such Series A
Junior Subordinated Debentures, on behalf of such holder, into shares of
American General Common Stock.  The Written Action also provides that, if such
Series A Preferred Securities and notice of conversion are so delivered (or
transferred, in the case of book-entry Series A Preferred Securities) to the
Conversion Agent before the close of business on the Conversion Expiration Date,
American General Delaware shall deliver the appropriate portion of the Series A
Junior Subordinated Debentures held by it to the Conversion Agent for conversion
in accordance with this Section.  As promptly as practicable after its receipt
of a copy of such notice of conversion and the certificates representing the
Series A Junior Subordinated Debentures surrendered for conversion (or, in the
case of book-entry Series A Junior Subordinated Debentures, the transfer of such
Series A Junior Subordinated Debentures to its account at the Depository), the
Company shall issue and deliver at the office of the Conversion Agent a
certificate or certificates for the number of full shares of American General
Common Stock issuable upon such conversion, together with the cash payment, if
any, in lieu of any fraction of a share to the Person or Persons entitled to
receive the same and, if required pursuant to Section 11(e) below, the Series A
Junior Subordinated Debentures referenced in such section.

          (c) Conversion Procedure After Series A Special Event Exchange.  In
order to convert Series A Junior Subordinated Debentures into shares of American
General Common Stock after a Series A Special Event Exchange and prior to the
Conversion Expiration Date of the Series A Junior Subordinated Debentures, the
Holder of any Series A Junior Subordinated Debentures to be converted shall
surrender to the Conversion Agent such Series A Junior Subordinated Debentures,
duly endorsed or assigned to the Company or in blank (or, if such Series A
Junior Subordinated Debentures are in book-entry form, cause such Series A
Junior Subordinated Debentures to be transferred to the account of the
Conversion Agent on the records of the Depository), together with an irrevocable
notice of conversion (copies of which shall be available at the office of the
Conversion Agent) stating that the Holder elects to convert such Series A Junior
Subordinated Debentures or, if less than the entire principal amount thereof is
to be converted, the portion thereof to be converted.  Such notice of conversion
shall list the name or names, if other than the Holder, in which the shares of
American General Common Stock to be issued upon conversion are to be registered
upon conversion (and in which the unconverted portion, if any, of the Series A
Junior Subordinated Debentures surrendered are to be registered).  As promptly
as practicable after its receipt of a copy of such notice of conversion and the
certificates representing the Series A Junior Subordinated Debentures
surrendered for conversion (or, in the case of book-entry Series A Junior
Subordinated Debentures, the transfer of such Series A Junior Subordinated
Debentures to its account at the Depository), the Company shall issue and shall
deliver at the office of the

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Conversion Agent a certificate or certificates for the number of full shares of
American General Common Stock issuable upon such conversion, together with the
cash payment, if any, in lieu of any fraction of a share, and, if applicable, a
new Series A Junior Subordinated Debenture representing the unconverted portion
of the Series A Junior Subordinated Debentures surrendered for conversion.

          (d) Fractional Shares.  No fractional shares of American General
Common Stock will be issued as a result of conversion, but in lieu thereof, such
fractional interest will be paid in cash (computed to the nearest cent, with
one-half cent being rounded upward) by the Company based on the Current Market
Price (as defined in Section 12(d)) of American General Common Stock on the date
the notice of conversion was received by the Conversion Agent.

          (e) Partial Conversions.  If the conversion of any Series A Junior
Subordinated Debenture is in part only, then a new Series A Junior Subordinated
Debenture for the unconverted portion thereof will be issued in the name of the
Holder thereof (or, subject to compliance with applicable legal requirements,
the name specified by the Holder) upon the cancellation thereof in accordance
with Section 305 of the Indenture.

          (f) No Payments.  Subject to the next succeeding sentence, upon the
conversion of any Series A Junior Subordinated Debentures into American General
Common Stock, the Company will not make, or be required to make, any payment,
allowance or adjustment for accrued interest (including any Additional Interest)
thereon, whether or not in arrears.  If, however, a notice of conversion is
received by the Conversion Agent with respect to Series A Junior Subordinated
Debentures on or after a Regular Record Date and prior to the next succeeding
Interest Payment Date, the Holder thereof will be entitled to receive the
interest payable on such Interest Payment Date on the portion of such Series A
Junior Subordinated Debentures to be converted, notwithstanding the conversion
thereof prior to such Interest Payment Date.  No payment or adjustment shall be
made upon conversion of any Series A Junior Subordinated Debentures into
American General Common Stock with respect to dividends or other distributions
on such American General Common Stock having record dates prior to the date of
conversion.

          (g) Effective Time of Conversion.  Each conversion shall be deemed to
have been effected immediately prior to the close of business on the day on
which the related notice of conversion was received by the Conversion Agent and
the Conversion Price of Series A Subordinated Debentures surrendered for
conversion shall be the Conversion Price in effect at that time.  The Person or
Persons entitled to receive the American General Common Stock issuable upon such
conversion shall be treated for all purposes as the record holder or holders of
the American General Common Stock issued upon such conversion as of such
effective time and, at such time, the rights of the Holders of the converted
Series A Junior Subordinated Debentures, as such Holders, but subject to the
second sentence of Section 11(f) and the last sentence of Section 11(h), shall
cease.

          (h) Effect of Conversion.  Subject to the second sentence of Section
11(f), the Company's delivery (through the Conversion Agent or otherwise) of the
number of full

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shares of American General Common Stock into which the Series A Junior
Subordinated Debentures surrendered for conversion are convertible (together
with the cash payment, if any, in lieu of fractional shares) to the Person or
Persons entitled to receive such shares shall be deemed to satisfy the Company's
obligation to pay the principal amount at Maturity of the portion of Series A
Junior Subordinated Debentures so converted and any unpaid interest, including
Additional Interest (but excluding Additional Amounts), accrued on, or payable
with respect to, such Series A Junior Subordinated Debentures at the time of
such conversion.  A Holder's right to receive Additional Amounts accrued as of
the effective time of conversion shall continue until such Additional Amounts
are paid.

          (i) Issuance of Rights.  Whenever the Company shall issue shares of
American General Common Stock upon conversion of Series A Junior Subordinated
Debentures as contemplated by this Section 11, the Company shall issue, together
with each such share of American General Common Stock, one right to purchase
Series A Junior Participating Preferred Stock of the Company (or other
securities in lieu thereof) pursuant to the Rights Agreement, dated as of July
27, 1989, between the Company and First Chicago Trust Company of New York, as
amended, or any similar rights issued to holders of American General Common
Stock in addition thereto or in replacement therefor (such rights, together with
any additional or replacement rights, being collectively referred to as the
"Rights"), whether or not such Rights shall be exercisable at such time, but
only if such Rights are issued and outstanding and held by other holders of
American General Common Stock (or are evidenced by outstanding share
certificates representing American General Common Stock) at such time and have
not expired or been redeemed.

          12.  EXPIRATION OF CONVERSION RIGHTS.

          (a) Right of Company to Terminate Conversion Privilege.  On or after
May 31, 2000, the Company may, at its option, cause the conversion rights of
Holders of Series A Junior Subordinated Debentures to expire if (i) the Company
is then current in the payment of interest (without regard to any Extension
Period) on the Series A Junior Subordinated Debentures and (ii) for 20 Trading
Days (as defined in Section 13(e)) within any period of 30 consecutive Trading
Days, including the last Trading Day of such period, the Current Market Price of
American General Common Stock shall have exceeded 120% of the Conversion Price
then in effect.

          (b) Exercise of Option Prior to a Series A Special Event Exchange.  In
order to exercise its conversion expiration option prior to a Series A Special
Event Exchange, the Company shall give a written notice to American General
Delaware directing American General Delaware to exercise its right, pursuant to
Section 8(d) of the Written Action, to cause the conversion rights of the
holders of Series A Preferred Securities to expire and to issue the press
release referred to in Section 8(d)(ii) of the Written Action.  The Company
shall also furnish a copy of such notice to the Trustee (and the Conversion
Agent if the Trustee is not then serving as the Conversion Agent).  If American
General Delaware fails to issue such press release within two Business Days
after its receipt of such notice, the Company may, on behalf of American General
Delaware, issue such press release in accordance with the provisions of Section
8(d)(ii) of the Written Action.

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          (c) Exercise of Option After a Series A Special Event Exchange.  In
order to exercise its conversion expiration option after a Series A Special
Event Exchange, the Company shall issue a press release for publication on the
Dow Jones News Service or on a comparable news service announcing the Conversion
Expiration Date of the Series A Junior Subordinated Debentures.  Such press
release must be issued prior to the opening of business on the second Trading
Day after a period in which the conditions in Section 12(a) have been met, but
in no event prior to May 31, 2000.  Such press release shall state that the
Company has elected to exercise its right to terminate the conversion privilege,
specify the Conversion Expiration Date of the Series A Junior Subordinated
Debentures (as determined in the manner set forth below) and provide the
Conversion Price and the Current Market Price of American General Common Stock,
in each case as of the close of business on the Trading Day next preceding the
date of the press release.  Additionally, the Company shall cause a notice of
the expiration of conversion rights (a "Notice of Conversion Expiration") to be
given by first-class mail to the Holders of Series A Junior Subordinated
Debentures, the Trustee (and the Conversion Agent if the Trustee is not then
serving as the Conversion Agent) not more than four Business Days after the
Company issues the press release.  The Notice of Conversion Expiration shall
state, as appropriate:  (i) the Conversion Expiration Date of the Series A
Junior Subordinated Debentures; (ii) the Conversion Price of the Series A Junior
Subordinated Debentures and the Current Market Price of the American General
Common Stock, in each case as of the close of business on the Trading Day next
preceding the date of the Notice of Conversion Expiration; (iii) the place or
places at which a conversion notice with respect to Series A Junior Subordinated
Debentures may be given to the Conversion Agent in accordance with Section 11(c)
prior to the Conversion Expiration Date of the Series A Junior Subordinated
Debentures; and (iv) such other information or instructions as the Company deems
necessary or advisable to enable a Holder to exercise its conversion right
hereunder.  Notice of Conversion Expiration shall be deemed to have been given
on the day such notice is first mailed by first-class mail, postage prepaid, to
each Holder of Series A Junior Subordinated Debentures at the address of the
Holder appearing in the Security Register (whether or not the Holder receives
the Notice of Conversion Expiration).  No defect in the Notice of Conversion
Expiration or in the mailing thereof with respect to any Series A Junior
Subordinated Debenture shall affect the validity of the Company's exercise of
its conversion expiration option if the press release referred to above shall
have been issued.

          (d) Certain Definitions.  The term "Conversion Expiration Date" has
the meaning assigned to such term in Section 8(d)(ii) of the Written Action.
The "Conversion Expiration Date of the Series A Junior Subordinated Debentures"
shall be the close of business on the Business Day selected by the Company which
is  not less than 30 nor more than 60 calendar days after the date on which the
Company issues the press release required by Section 12(c) announcing its
intention to terminate the conversion rights of the holders of the Series A
Junior Subordinated Debentures.  If the Company does not exercise its conversion
expiration option, the Conversion Expiration Date of the Series A Junior
Subordinated Debentures (i) with respect to any principal amount of Series A
Junior Subordinated Debentures which is called for redemption shall be the close
of business on the third Business Day prior to the scheduled Redemption Date for
such Series A Junior Subordinated Debentures and (ii) in any other case shall be
the close of business on the

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third Business Day prior to the Stated Maturity of the principal of the Series A
Junior Subordinated Debentures.  As of the close of business on the earlier of
the Conversion Expiration Date or the Conversion Expiration Date of the Series A
Junior Subordinated  Debentures, the Series A Junior Subordinated Debentures
shall be deemed to be non-convertible securities.

          The term "Current Market Price" of American General Common Stock for
any day means the reported last sale price, regular way, on such day, or, if no
sale takes place on such day, the average of the reported closing bid and asked
prices on such day, regular way, in either case as reported on the NYSE
Composite Tape, or, if the American General Common Stock is not listed or
admitted to trading on the NYSE, on the principal national securities exchange
on which the American General Common Stock is listed or admitted to trading, or
if the American General Common Stock is not listed or admitted to trading on a
national securities exchange, on the National Market System of the National
Association of Securities Dealers, Inc., or, if the American General Common
Stock is not quoted or admitted to trading on such quotation system, on the
principal quotation system on which the American General Common Stock is listed
or admitted to trading or quoted, or, if not listed or admitted to trading or
quoted on any national securities exchange or quotation system, the average of
the closing bid and asked prices of the American General Common Stock in the
over-the-counter market on the day in question as reported by the National
Quotation Bureau Incorporated, or a similar generally accepted reporting
service, or, if not so available in such manner, as furnished by any NYSE member
firm selected from time to time by the Board of Directors of the Company for
that purpose or, if not so available in such manner, as otherwise determined in
good faith by the Company's Board of Directors.

          13.  CONVERSION PRICE ADJUSTMENTS.

          (a) Stock Dividends, Subdivisions, Etc.  The Conversion Price shall be
subject to adjustment from time to time as follows:

          (i) If the Company shall pay or make a dividend or other distribution
     exclusively in American General Common Stock on any class or series of
     capital stock of the Company, then the Conversion Price in effect at the
     opening of business on the day following the date fixed for the
     determination of shareholders entitled to receive such dividend or other
     distribution shall be reduced by multiplying such Conversion Price by a
     fraction, of which the numerator shall be the number of shares of American
     General Common Stock outstanding at the close of business on the date fixed
     for such determination and the denominator shall be the sum of such number
     of shares and the total number of shares constituting such dividend or
     other distribution, such reduction to become effective immediately after
     the opening of business on the day following the date fixed for such
     determination.  For the purposes of this subparagraph (i), the number of
     shares of American General Common Stock at any time outstanding shall not
     include shares held in the treasury of the Company.  The Company shall not
     pay any dividend or make any distribution exclusively in American General
     Common Stock on shares of any class or series of capital stock of the
     Company held in the treasury of the Company.

                                       10
<PAGE>
 
          (ii) Subject to Section 13(g), if the Company shall pay or make a
     dividend or other distribution on the outstanding shares of American
     General Common Stock consisting exclusively of, or shall otherwise issue to
     all holders of the outstanding shares of American General Common Stock,
     rights (other than Rights) or warrants entitling the holders thereof to
     subscribe for or purchase shares of American General Common Stock at a
     price per share (taking into account the consideration received for the
     issuance of such right or warrant plus any consideration to be received
     upon the exercise thereof) less than the Current Price per share
     (determined as provided in subparagraph (vi) of this Section 13(a)) of the
     American General Common Stock on the date fixed for the determination of
     shareholders entitled to receive such rights or warrants, then the
     Conversion Price in effect at the opening of business on the day following
     the date fixed for such determination shall be reduced by multiplying such
     Conversion Price by a fraction, of which the numerator shall be the number
     of shares of American General Common Stock outstanding at the close of
     business on the date fixed for such determination plus the number of shares
     of American General Common Stock which the aggregate of the offering price
     of the total number of shares of American General Common Stock so offered
     for subscription or purchase would purchase at such Current Price per share
     and the denominator shall be the number of shares of American General
     Common Stock outstanding at the close of business on the date fixed for
     such determination plus the number of shares of American General Common
     Stock so offered for subscription or purchase, such reduction to become
     effective immediately after the opening of business on the day following
     the date fixed for such determination. For the purposes of this
     subparagraph (ii), the number of shares of American General Common Stock at
     any time outstanding shall not include shares held in the treasury of the
     Company. The Company shall not issue any rights or warrants in respect of
     shares of American General Common Stock held in the treasury of the
     Company. In case any rights or warrants referred to in this subparagraph
     (ii) in respect of which an adjustment shall have been made shall expire or
     terminate unexercised, the Conversion Price shall be readjusted at the time
     of such expiration to the Conversion Price that would have been in effect
     if no adjustment had been made on account of the distribution or issuance
     of such expired rights or warrants.

          (iii)  If outstanding shares of American General Common Stock shall be
     subdivided into a greater number of shares of American General Common
     Stock, then the Conversion Price in effect at the opening of business on
     the day following the day upon which such subdivision becomes effective
     shall be proportionately reduced and, conversely, if outstanding shares of
     American General Common Stock shall be combined into a smaller number of
     shares of American General Common Stock, then the Conversion Price in
     effect at the opening of business on the day following the day upon which
     such combination becomes effective shall be proportionately increased, such
     reduction or increase, as the case may be, to become effective immediately
     after the opening of business on the day following the day upon which such
     subdivision or combination becomes effective.

                                       11
<PAGE>
 
          (iv) Subject to the last sentence of this subparagraph (iv), if the
     Company shall, by dividend or otherwise, pay or otherwise distribute to all
     holders of American General Common Stock evidences of its indebtedness,
     shares of any class or series of American General Capital Stock, cash,
     securities or other assets other than Excluded Dividends (as defined
     below), then the Conversion Price shall be reduced so that the same shall
     equal the price determined by multiplying (A) the Conversion Price in
     effect immediately prior to the effectiveness of the Conversion Price
     reduction contemplated by this subparagraph (iv) by (B) a fraction of which
     the numerator shall be the Current Price per share (determined as provided
     in subparagraph (vi) of this Section 13(a)) of the American General Common
     Stock on the date fixed for the payment of such distribution (the
     "Reference Date") less the fair market value, on the Reference Date, of the
     portion of the evidences of indebtedness, shares of American General
     Capital Stock, cash, securities or other assets so distributed (other than
     Excluded Dividends) applicable to one share of American General Common
     Stock and the denominator shall be such Current Price per share of the
     American General Common Stock, such reduction to become effective
     immediately prior to the opening of business on the day following the
     Reference Date.   "Excluded Dividends" shall mean (1) any dividend or
     distribution referred to in subparagraph (i) of this Section 13(a), (2) any
     dividend, distribution or issuance of rights or warrants referred to in
     subparagraph (ii) of this Section 13(a) or of Rights, (3) any regular cash
     dividend on the American General Common Stock that does not exceed the per
     share amount of the immediately preceding regular cash dividend on the
     American General Common Stock (as adjusted to appropriately reflect any of
     the events referred to in subparagraphs (i) and (iii) of this Section
     13(a)), and (4) in the case of any other dividend or distribution (cash or
     otherwise), that portion thereof which, when combined with the per share
     fair market value of all other dividends and distributions paid by the
     Company on American General Common Stock during the 365-day period ending
     on the date of declaration of such dividend or distribution (as adjusted to
     appropriately reflect any of the events referred to in subparagraphs (i)
     and (iii) of this Section 13(a) and excluding dividends and distributions
     referred to in clauses (1) and (2) and dividends and distributions, or
     portions thereof, that resulted in an adjustment to the Conversion Price
     (or would have but for the application of Section 13(a)(viii), 13(f) or
     13(g)), does not exceed 15% of the Current Price per share of the American
     General Common Stock on the Trading Day immediately preceding the date of
     declaration of such dividend or distribution.  The fair market value of any
     dividend or distribution not paid in cash shall be  determined in good
     faith by the Board of Directors, whose determination shall be conclusive
     and described in a resolution of the Board of Directors.  For purposes of
     this subparagraph (iv), any dividend or distribution that includes shares
     of American General Common Stock or rights or warrants to subscribe for or
     purchase shares of American General Common Stock shall be deemed instead to
     be (1) a dividend or distribution of the evidences of indebtedness, shares
     of American General Capital Stock, cash or assets other than such shares of
     American General Common Stock or such rights or warrants (making any
     Conversion Price reduction required by this subparagraph (iv)) immediately
     followed by (2) a dividend or distribution of such shares of American
     General

                                       12
<PAGE>
 
     Common Stock or such rights or warrants (making any further Conversion
     Price reduction required by subparagraphs (i) or (ii) of this Section 13(a)
     and, in the case of rights or warrants, subject to the last sentence of
     such subparagraph (ii)), except (A) the Reference Date of such dividend or
     distribution as defined in this subparagraph (iv) shall be substituted as
     "the date fixed for the determination of shareholders entitled to receive
     such dividend or other distribution," "the date fixed for the determination
     of shareholders entitled to receive such rights or warrants" and "the date
     fixed for such determination" within the meaning of subparagraphs (i) and
     (ii) of this Section 13(a) and (B) any shares of American General Common
     Stock included in such dividend or distribution shall not be deemed
     "outstanding at the close of business on the date fixed for such
     determination" within the meaning of subparagraph (i) of this Section
     13(a).

          (v) If a tender or exchange offer made by the Company or any
     Subsidiary of the Company for all or any portion of American General Common
     Stock shall expire and such tender or exchange offer shall involve the
     payment by the Company or such Subsidiary of consideration per share of
     American General Common Stock having a fair market value (as determined in
     good faith by the Board of Directors, whose determination shall be
     conclusive and described in a Board Resolution) at the last time (the
     "Tender Expiration Time") tenders or exchanges may be made pursuant to such
     tender or exchange offer (as it may have been amended) that exceeds 110% of
     the Current Price per share (determined as provided in subparagraph (vi) of
     this Section 13(a)) of the American General Common Stock on the Trading Day
     (as defined in Section 13(e)) next succeeding the Tender Expiration Time,
     then the Conversion Price shall be reduced so that the same shall equal the
     price determined by multiplying the Conversion Price in effect immediately
     prior to the effectiveness of the Conversion Price reduction contemplated
     by this subparagraph (v) by a fraction, of which the numerator shall be the
     number of shares of American General Common Stock outstanding (including
     any tendered or exchanged shares) at the Tender Expiration Time multiplied
     by the Current Price per share (determined as provided in subparagraph (vi)
     of this Section 13(a)) of the American General Common Stock on the Trading
     Day next succeeding the Tender Expiration Time and the denominator shall be
     the sum of (x) the fair market value (determined as aforesaid) of the
     aggregate consideration payable to shareholders based on the acceptance (up
     to any maximum specified in the terms of the tender or exchange offer) of
     all shares validly tendered or exchanged and not withdrawn as of the Tender
     Expiration Time (the shares deemed so accepted, up to any such maximum,
     being referred to as the "Purchased Shares") and (y) the product of the
     number of shares of American General Common Stock outstanding (less any
     Purchased Shares) at the Tender Expiration Time and the Current Price per
     share (determined as provided in subparagraph (vi) of this Section 13(a))
     of the American General Common Stock on the Trading Day next succeeding the
     Tender Expiration Time, such reduction to become effective immediately
     prior to the opening of business on the day following the Tender Expiration
     Time.  Notwithstanding anything contained in this Section 13(a)(v) to the
     contrary, no adjustment shall be made to the Conversion Price in the case
     of a tender or exchange offer of the character described in Rule 13e-
     4(h)(5)

                                       13
<PAGE>
 
     under the Securities Exchange Act of 1934, as amended, or any successor
     rule thereto.

          (vi) For the purpose of any computation under subparagraphs (ii), (iv)
     and (v) of this Section 13(a), the "Current Price" per share of American
     General Common Stock on any date in question shall be deemed to be the
     average of the daily Closing Prices (as defined in Section 13(e)) for the
     five consecutive Trading Days selected by the Company commencing not more
     than 20 Trading Days before, and ending not later than, the earlier of the
     day in question and, if applicable, the day before the "ex" date with
     respect to the issuance or distribution requiring such computation;
     provided, however, that if another event occurs that would require an
     adjustment pursuant to subparagraph (i) through (v), inclusive, the Board
     of Directors may make such adjustments to the Closing Prices during such
     five Trading Day period as it deems appropriate to effectuate the intent of
     the adjustments in this Section 13(a), in which case any such determination
     by the Board of Directors shall be set forth in a Board Resolution and
     shall be conclusive.  For purposes of this paragraph, the term "ex" date,
     (1) when used with respect to any issuance or distribution, means the first
     date on which the American General Common Stock trades regular way on the
     relevant exchange or in the relevant market from which the Closing Prices
     were obtained without the right to receive such issuance or distribution,
     and (2) when used with respect to any tender or exchange offer means the
     first date on which the American General Common Stock trades regular way on
     such exchange or in such market after the Tender Expiration Time of such
     offer.

          (vii)  The Company may make such reductions in the Conversion Price of
     the Series A Junior Subordinated Debentures, in addition to those required
     by subparagraphs (i), (ii), (iii), (iv) and (v) of this Section 13(a), as
     it considers to be advisable to avoid or diminish any income tax to holders
     of American General Common Stock or holders of rights to acquire American
     General Common Stock or securities convertible into American General Common
     Stock, resulting from any dividend or distribution of stock (or rights to
     acquire stock) or from any event treated as such for income tax purposes.
     The Company from time to time may reduce the Conversion Price by any amount
     selected by the Company for any period of time if the period is at least
     twenty days, and the Board of Directors of the Company shall have made a
     determination that such reduction would be in the best interest of the
     Company, which determination shall be conclusive.  Whenever the Conversion
     Price is reduced pursuant to the preceding sentence, the Company shall mail
     to holders of record of the Series A Junior Subordinated Debentures a
     notice of the reduction at least fifteen days prior to the date the reduced
     Conversion Price takes effect, and such notice shall state the reduced
     Conversion Price and the period it will be in effect.

          (viii)  No adjustment in the Conversion Price shall be required unless
     such adjustment would require an increase or decrease of at least 1% in the
     Conversion Price; provided, however, that any adjustments which by reason
     of this subparagraph (viii) are not required to be made shall be carried
     forward and taken into account

                                       14
<PAGE>
 
     in any subsequent adjustment.  All calculations under this Section 13 shall
     be made to the nearest cent or to the nearest 1/100th of a share, as the
     case may be, with one-half cent and 5/1000th of a share, respectively,
     being rounded upward.

          (ix) Whenever the Conversion Price is adjusted as herein provided:

               (1) the Company shall compute the adjusted Conversion Price and
          shall prepare a certificate signed by the Chief Financial Officer, the
          Treasurer or a Vice President of the Company setting forth the
          adjusted Conversion Price and showing in reasonable detail the facts
          upon which such adjustment is based, and such certificate shall
          forthwith be filed with the Conversion Agent and, if such adjustment
          is made prior to a Series A Special Event Exchange, to American
          General Delaware; and

               (2) if such adjustment is made after a Series A Special Event
          Exchange, the Company shall cause a notice stating that the Conversion
          Price has been adjusted and setting forth the adjusted Conversion
          Price to be mailed to all record holders of Series A Junior
          Subordinated Debentures at their last addresses as they appear upon
          the Security Register.

     (b) Reclassification, Consolidation, Merger Or Sale of Assets.  In the
event that the Company shall be a party to any transaction, including without
limitation any recapitalization or reclassification of the American General
Common Stock (other than a change in par value, or from par value to no par
value, or from no par value to par value, or as a result of a subdivision or
combination of the American General Common Stock), any consolidation of the
Company with, or merger of the Company into, any other Person, any merger of
another Person into the Company (other than a merger which does not result in a
reclassification, conversion, exchange or cancellation of outstanding shares of
American General Common Stock), any sale or transfer of all or substantially all
of the assets of the Company or any compulsory share exchange, in each case
pursuant to which the American General Common Stock is converted into the right
to receive other securities, cash or other property, then lawful provision shall
be made as part of the terms of such transaction whereby each holder of Series A
Junior Subordinated Debentures then outstanding shall have the right thereafter
to convert such Series A Junior Subordinated Debentures only into (i) in the
case of any such transaction other than a Common Stock Fundamental Change (as
defined in Section 13(e)), the kind and amount of securities, cash and other
property receivable upon the consummation of such transaction by a holder of
that number of shares of American General Common Stock into which such Series A
Junior Subordinated Debentures could have been converted immediately prior to
such transaction, after giving effect, in the case of any Non-Stock Fundamental
Change (as defined in Section 13(e)), to any adjustment in the Conversion Price
required by the provisions of Section 13(d), and (ii) in the case of a Common
Stock Fundamental Change, common stock of the kind received by holders of
American General Common Stock as a result of such Common Stock Fundamental
Change in an amount determined pursuant to the provisions of Section 13(d).  The
Company or the Person formed by such consolidation or resulting from such merger
or which acquired such assets or which acquired the Company's shares, as the
case may be,

                                       15
<PAGE>
 
shall make provision in its certificate or articles of incorporation or other
constituent document to establish such right.  Such certificate or articles of
incorporation or other constituent document shall provide for adjustments which,
for events subsequent to the effective date of such provisions in such
certificate or articles of incorporation or other constituent document, shall be
as nearly equivalent as may be practicable to the adjustments provided for in
this Section 13.  The above provisions shall similarly apply to successive
transactions of the foregoing type.

     (c) Prior Notice Of Certain Events.  In case:

          (i) the Company shall (1) declare any dividend (or any other
     distribution) on the American General Common Stock, other than (A) a
     dividend payable in shares of American General Common Stock or (B) a
     dividend payable in cash that would not require an adjustment pursuant to
     13(a)(iv) or (2) authorize a tender or exchange offer that would require an
     adjustment pursuant to Section 13(a)(v);

          (ii) the Company shall authorize the granting to all holders of
     American General Common Stock of rights or warrants to subscribe for or
     purchase any shares of stock of any class or series or of any other rights
     or warrants (other than Rights);

          (iii)  of any reclassification of American General Common Stock (other
     than a subdivision or combination of the outstanding American General
     Common Stock, or a change in par value, or from par value to no par value,
     or from no par value to par value), or of any consolidation or merger to
     which the Company is a party and for which approval of any shareholders of
     the Company shall be required, or of the sale or transfer of all or
     substantially all of the assets of the Company or of any compulsory share
     exchange whereby the American General Common Stock is converted into other
     securities, cash or other property; or

          (iv) of the voluntary or involuntary dissolution, liquidation or
     winding up of the Company;

then the Company shall (1) if such event occurs prior to a Series A Special
Event Exchange, cause to be filed with American General Delaware or (2) if such
event occurs after a Series A Special Event Exchange, cause to be mailed to the
Holders at their last addresses as they appear in the Security Register, in each
case, at least fifteen calendar days prior to the applicable record or effective
date hereinafter specified, a notice stating (x) the date on which a record (if
any) is to be taken for the purpose of such dividend, distribution, rights or
warrants or, if a record is not to be taken, the date as of which the holders of
American General Common Stock of record to be entitled to such dividend,
distribution, rights or warrants are to be determined or (y) the date on which
such reclassification, consolidation, merger, sale, transfer, share exchange,
dissolution, liquidation or winding up is expected to become effective, and the
date as of which it is expected that holders of American General Common Stock of
record shall be entitled to exchange their shares of American General Common
Stock for securities, cash or other property deliverable upon such
reclassification, consolidation, merger, sale,transfer, share exchange,
dissolution, liquidation or winding up

                                       16
<PAGE>
 
(but no failure to mail such notice or any defect therein or in the mailing
thereof shall affect the validity of the corporate action required to be
specified in such notice).

     (d) Adjustments In Case of Fundamental Changes.  Notwithstanding any other
provision in this Section 13 to the contrary, if any Fundamental Change (as
defined in Section 13(e)) occurs, then the Conversion Price in effect will be
adjusted immediately after such Fundamental Change as described below.  In
addition, in the event of a Common Stock Fundamental Change, the Series A Junior
Subordinated Debentures shall be convertible solely into common stock of the
kind received by holders of American General Common Stock as the result of such
Common Stock Fundamental Change as more specifically provided in the following
clauses (d)(i) and (d)(ii).

For purposes of calculating any adjustment to be made pursuant to this Section
13(d) in the event of a Fundamental Change, immediately after such Fundamental
Change:

          (i) in the case of a Non-Stock Fundamental Change, the Conversion
     Price shall thereupon become the lower of (A) the Conversion Price in
     effect immediately prior to such Non-Stock Fundamental Change, but after
     giving effect to any other prior adjustments effected pursuant to this
     Section 13, and (B) the result obtained by multiplying the greater of the
     Applicable Price (as defined in Section 13(e)) or the then applicable
     Reference Market Price (as defined in Section 13(e)) by a fraction, of
     which the numerator shall be $50 and the denominator shall be the amount
     set forth below (based on the date such Non-Stock Fundamental Change
     occurs):
<TABLE>
<CAPTION>
 
          Twelve Months
          Ending May 31,           Denominator
<S>                                <C>
 
          1996.................      $53.000
          1997.................      $52.625
          1998.................      $52.250
          1999.................      $51.875
          2000.................      $51.500
          2001.................      $51.125
          2002.................      $50.750
          2003.................      $50.375
          2004 and thereafter..      $50.000
</TABLE>
          ; and

          (ii) in the case of a Common Stock Fundamental Change, the Conversion
     Price in effect immediately prior to such Common Stock Fundamental Change,
     but after giving effect to any other prior adjustments effected pursuant to
     this Section 13, shall thereupon be adjusted by multiplying such Conversion
     Price by a fraction of which the numerator shall be the Purchaser Stock
     Price (as defined in Section 13(e)) and the denominator shall be the
     Applicable Price; provided, however, that in the event of a Common Stock
     Fundamental Change in which (A) 100% of the value of

                                       17
<PAGE>
 
     the consideration received by a holder of American General Common Stock is
     common stock of the successor, acquiror or other third party (and cash, if
     any, is paid only with respect to any fractional interests in such common
     stock resulting from such Common Stock Fundamental Change) and (B) all of
     the American General Common Stock shall have been exchanged for, converted
     into or acquired for common stock (and cash with respect to fractional
     interests) of the successor, acquiror or other third party, the Conversion
     Price of the Series A Junior Subordinated Debentures in effect immediately
     prior to such Common Stock Fundamental Change shall thereupon be adjusted
     by multiplying such Conversion Price by a fraction of which the numerator
     shall be one (1) and the denominator shall be the number of shares of
     common stock of the successor, acquiror, or other third party received by a
     holder of one share of American General Common Stock as a result of such
     Common Stock Fundamental Change.

     (e) Definitions.  The following definitions shall apply to terms used in
this Section 13:

          (i) "Applicable Price" shall mean (i) in the event of a Non-Stock
     Fundamental Change in which the holders of the American General Common
     Stock receive only cash, the amount of cash received by a holder of one
     share of American General Common Stock and (ii) in the event of any other
     Non-Stock Fundamental Change or any Common Stock Fundamental Change, the
     average of the Closing Prices of the American General Common Stock for the
     ten consecutive Trading Days prior to and including the record date for the
     determination of the holders of American General Common Stock entitled to
     receive securities, cash or other property in connection with such Non-
     Stock Fundamental Change or Common Stock Fundamental Change, or, if there
     is no such record date, the date upon which the holders of the American
     General Common Stock shall have the right to receive such securities, cash
     or other property (such record date or distribution date being hereinafter
     referred to as the "Entitlement Date"), in each case, as adjusted in good
     faith by the Board of Directors to appropriately reflect any of the events
     referred to in subparagraphs (i), (ii), (iii), (iv) and (v) of Section
     13(a).

          (ii) "Closing Price" of any common stock on any day shall mean the
     reported last sale price, regular way, on such day, or, if no sale takes
     place on such day, the average of the reported closing bid and asked prices
     on such day, regular way, in either case as reported on the principal
     national securities exchange on which such common stock is listed or
     admitted to trading, or, if such common stock is not listed or admitted to
     trading on a national securities exchange, on the National Market System of
     the National Association of Securities Dealers, Inc., or, if such common
     stock is not quoted or admitted to trading on such quotation system, on the
     principal quotation system on which such common stock is listed or admitted
     to trading or quoted, or, if not listed or admitted to trading or quoted on
     any national securities exchange or quotation system, the average of the
     closing bid and asked prices of such common stock in the over-the-counter
     market on the day in question as reported by the National Quotation Bureau
     Incorporated, or a similar generally

                                       18
<PAGE>
 
     accepted reporting service, or, if not so available in such manner, as
     furnished by any NYSE member firm selected from time to time by the Board
     of Directors for that purpose or, if not so available in such manner, as
     otherwise determined in good faith by the Board of Directors.

          (iii)  "Common Stock Fundamental Change" shall mean any Fundamental
     Change in which more than 50% of the value (as determined in good faith by
     the Board of Directors) of the consideration received by holders of
     American General Common Stock consists of common stock that for each of the
     ten consecutive Trading Days prior to the Entitlement Date has been
     admitted for listing or admitted for listing subject to notice of issuance
     on a national securities exchange or quoted on the National Market System
     of the National Association of Securities Dealers, Inc.; provided, however,
     that a Fundamental Change shall not be a Common Stock Fundamental Change
     unless either (i) the Company continues to exist after the occurrence of
     such Fundamental Change and the outstanding Series A Junior Subordinated
     Debentures continue to exist as outstanding Series A Junior Subordinated
     Debentures, or (ii) not later than the occurrence of such Fundamental
     Change, the outstanding Series A Junior Subordinated Debentures are
     converted into or exchanged for convertible subordinated debentures of the
     entity succeeding to the business of the Company, which convertible
     subordinated debentures have terms substantially similar to those of the
     Series A Junior Subordinated Debentures.

          (iv) "Conversion Price" shall have the meaning given that term in
     Section 11(a).

          (v) "Fundamental Change" shall mean the occurrence of any transaction
     or event in connection with a plan pursuant to which all or substantially
     all of the American General Common Stock shall be exchanged for, converted
     into, acquired for or constitute solely the right to receive securities,
     cash or other property (whether by means of an exchange offer, liquidation,
     tender offer, consolidation, merger, combination, reclassification,
     recapitalization or otherwise); provided, however, that, in the case of a
     plan involving more than one such transaction or event, for purposes of
     adjustment of the Conversion Price, such Fundamental Change shall be deemed
     to have occurred when substantially all of the American General Common
     Stock shall be exchanged for, converted into, or acquired for or constitute
     solely the right to receive securities, cash or other property, but the
     adjustment shall be based upon the highest weighted average per share
     consideration that a holder of American General Common Stock could have
     received in such transactions or events as a result of which more than 50%
     of the American General Common Stock shall have been exchanged for,
     converted into, or acquired for or constitute solely the right to receive
     securities, cash or other property.

          (vi) "Non-Stock Fundamental Change" shall mean any Fundamental Change
     other than a Common Stock Fundamental Change.

                                       19
<PAGE>
 
          (vii)  "Purchased Shares" shall have the meaning given that term in
     Section 13(a)(v).

          (viii)  "Purchaser Stock Price" shall mean, with respect to any Common
     Stock Fundamental Change, the average of the daily Closing Prices of the
     common stock received in such Common Stock Fundamental Change for the ten
     consecutive Trading Days prior to and including the Entitlement Date, as
     adjusted in good faith by the Board of Directors to appropriately reflect
     any of the events referred to in subparagraphs (i), (ii), (iii), (iv) and
     (v) of Section 13(a).

          (ix) "Reference Date" shall have the meaning given that term in
     Section 13(a)(iv).

          (x) "Reference Market Price" shall initially mean $22.42 and in the
     event of any adjustment to the Conversion Price other than as a result of a
     Non-Stock Fundamental Change, the Reference Market Price shall also be
     adjusted so that the ratio of the Reference Market Price to the Conversion
     Price after giving effect to any such adjustment shall always be the same
     as the ratio of $22.42 to the initial Conversion Price.

          (xi) "Tender Expiration Time" shall have the meaning given that term
     in Section 13(a)(v).

          (xii)  "Trading Day" shall mean, with respect to any security listed
     or admitted to trading on the NYSE, any day on which such security is
     traded on the NYSE, or, if such security is not listed or admitted to
     trading on the NYSE, on the principal national securities exchange on which
     such security is listed or admitted to trading, or, if such security is not
     listed or admitted to trading on a national securities exchange, on the
     National Market System of the National Association of Securities Dealers,
     Inc., or, if such security is not quoted or admitted to trading on such
     quotation system, on the principal quotation system on which such security
     is listed or admitted to trading or quoted, of, if not listed or admitted
     to trading or quoted on any national securities exchange or quotation
     system, in the over-the-counter market.

     (f) Dividend or Interest Reinvestment Plans.  Notwithstanding the foregoing
provisions of this Section 13, no adjustment of the Conversion Price shall be
required to be made upon the issuance of any shares of American General Common
Stock pursuant to any present or future plan providing for the reinvestment of
dividends or interest payable on securities of the Company and the investment of
additional optional amounts in shares of American General Common Stock under any
such plan, or the issuance of any shares of American General Common Stock or
options or rights to purchase such shares pursuant to any present or future
employee, officer, director, or consultant benefit plan or program or agreement
of the Company or a Subsidiary or pursuant to any option, warrant, right or
exercisable, exchangeable or convertible security outstanding as of the date the
Series A Junior Subordinated Debentures were first established pursuant to this
instrument.

                                       20
<PAGE>
 
     (g) Certain Rights.  Notwithstanding any other provision of this Section
13, the issuance or distribution of Rights shall not be deemed to constitute an
issuance or a distribution or dividend of rights, warrants, or other securities
to which any of the adjustment provisions described above applies.

     (h) Certain Additional Rights.  In case the Company shall, by dividend or
otherwise, declare or make a distribution on American General Common Stock
referred to in Section 13(a)(iv) (including, without limitation, dividends or
distributions referred to in the last sentence of Section 13(a)(iv) but
excluding the Excluded Dividends), the Holders of the Series A Junior
Subordinated Debentures, upon the conversion thereof subsequent to the close of
business on the date fixed for the determination of shareholders entitled to
receive such distribution and prior to the effectiveness of the Conversion Price
adjustment in respect of such distribution, shall also be entitled to receive
for each share of American General Common Stock into which the Series A Junior
Subordinated Debentures are converted, the portion of the shares of American
General Common Stock, rights, warrants, evidences of indebtedness, shares of
capital stock, cash and assets so distributed applicable to one share of
American General Common Stock; provided, however, that, at the election of the
Company (whose election shall be evidenced by a Board Resolution) with respect
to all Holders so converting, the Company may, in lieu of distributing to such
Holders any portion of such distribution not consisting of cash or securities of
the Company, pay such Holders an amount in cash equal to the fair market value
thereof (as determined in good faith by the Board of Directors, whose
determination shall be conclusive and described in a Board Resolution).  If any
conversion of Series A Junior Subordinated Debentures described in the
immediately preceding sentence occurs prior to the payment date for a
distribution to holders of American General Common Stock which the Holder of the
Series A Junior Subordinated Debentures so converted is entitled to receive in
accordance with the immediately preceding sentence, the Company may elect (such
election to be evidenced by a Board Resolution) to distribute to such Holder a
due bill for the shares of American General Common Stock, rights, warrants,
evidences of indebtedness, shares of capital stock, cash or assets to which such
Holder is so entitled, provided that such due bill (i) meets any applicable
requirements of the principal national securities exchange or other market on
which the American General Common Stock is then traded, and (ii) requires
payment or delivery of such shares of American General Common Stock, rights,
warrants, evidences of indebtedness, shares of capital stock, cash or assets no
later than the date of payment or delivery thereof to holders of shares of
American General Common Stock receiving such distribution.

     (i) One Adjustment.  There shall be no adjustment of the Conversion Price
in case of the issuance of any American General Capital Stock (or securities
convertible into or exchangeable for American General Capital Stock) or any
other distribution or event except as specifically described in this Section 13.
If any action would require adjustment of the Conversion Price pursuant to more
than one of the provisions of this Section 13, only one adjustment shall be made
and such adjustment shall be the amount of adjustment that has the highest
absolute value to the Holders of the Series A Junior Subordinated Debentures.

                                       21
<PAGE>
 
     14.  CONVERSION FOR AMERICAN GENERAL SERIES A PREFERRED STOCK PRIOR TO A
SERIES A SPECIAL EVENT EXCHANGE.

     (a) Convertibility.  Section 9 of the Written Action provides that, upon
the occurrence of an Exchange Event (as defined in Section 14(d)) prior to a
Series A Special Event Exchange, the holders of a majority of the aggregate
liquidation preference of the Series A Preferred Securities then outstanding,
voting at a meeting of the holders of the Series A Preferred Securities called
for such purpose or by written consent, may, at their option, direct the
Conversion Agent to exchange all (but not less than all) of the Series A
Preferred Securities for Series A Junior Subordinated Debentures and to
immediately convert such Series A Junior Subordinated Debentures, on behalf of
such holders, for shares of Series A Cumulative Convertible Preferred Stock, par
value $1.50 per share, of the Company ("American General Series A Preferred
Stock"), at the rate of one share of American General Series A Preferred Stock
for each $50 principal amount of Series A Junior Subordinated Debentures.
Accordingly, prior to a Series A Special Event Exchange and if any Series A
Preferred Securities are then outstanding, the Series A Junior Subordinated
Debentures shall be convertible at the request of Holders thereof, following an
Exchange Election (as defined in Section 9(c) of the Written Action) by a
majority in aggregate liquidation preference of the Series A Preferred
Securities, into fully paid and non-assessable shares of American General Series
A Preferred Stock in accordance with the terms and conditions of this Section
14.

     (b) Conversion Procedure.  The procedure for the conversion of all the
Series A Junior Subordinated Debentures into shares of American General Series A
Preferred Stock pursuant to this Section 14 shall be as follows:

          (i) The Conversion Agent, upon receiving irrevocable notice from
     American General Delaware (or such other Person as is entitled to give such
     notice under the Written Action) of an Exchange Election by the holders of
     a majority in aggregate liquidation preference of the Series A Preferred
     Securities (a "Notice of Exchange"), shall (A) exchange all (but not less
     than all) outstanding Series A Preferred Securities for Series A Junior
     Subordinated Debentures held by American General Delaware in the manner
     prescribed in Section 9(a) of the Written Action at the rate of $50
     principal amount of Series A Junior Subordinated Debentures for each share
     of Series A Preferred Securities and (B) deliver a copy of the Notice of
     Exchange to the Company and, if the Trustee is not then serving as the
     Conversion Agent, the Trustee.  Upon receipt by it of the Notice of
     Exchange, American General Delaware shall deliver the appropriate principal
     amount of Series A Junior Subordinated Debentures held by it to the
     Conversion Agent (or, if such Series A Junior Subordinated Debentures are
     in book-entry form, cause such principal amount of Series A Junior
     Subordinated Debentures to be transferred to the account of the Conversion
     Agent on the records of the Depository) for conversion in accordance with
     this Section 14.

          (ii) Upon receipt of a copy of the Notice of Election from the
     Conversion Agent and the certificates, if any, representing the appropriate
     principal amount of

                                       22
<PAGE>
 
     Series A Junior Subordinated Debentures held by American General Delaware
     (or the transfer thereof to its account at the Depository, as the case may
     be), the Company shall issue, and deliver to the Conversion Agent, shares
     of American General Series A Preferred Stock for the principal amount of
     Series A Junior Subordinated Debentures so to be converted, at the rate of
     one share of American General Series A Preferred Stock for each $50
     principal amount of Series A Junior Subordinated Debentures.

          (iii)  The Company shall cause the shares of American General Series A
     Preferred Stock issuable upon conversion of the Series A Junior
     Subordinated Debentures to be registered in the names of the holders of
     Series A Preferred Securities designated in the Notice of Exchange and, as
     promptly as practicable after receipt of certificates representing the
     shares of American General Series A Preferred Stock so registered, the
     Conversion Agent shall deliver such certificates, if any, representing the
     American General Series A Preferred Stock issuable upon such conversion to
     the Person or Persons entitled to receive the same.

     (c) Accrued Interest; Effective Date of Exchange.  Any accrued but unpaid
interest (including any Additional Interest) on the Series A Junior Subordinated
Debentures surrendered for conversion shall, from and after the time of such
conversion, be treated as accumulated and unpaid dividends on the American
General Series A Preferred Stock issued upon conversion of the Series A Junior
Subordinated Debentures.  Series A Junior Subordinated Debentures shall be
deemed to have been converted immediately prior to the close of business on the
Exchange Election Date (as defined below).  The Person or Persons entitled to
receive the American General Series A Preferred Stock issuable upon an exchange
of the Series A Preferred Securities shall be treated for all purposes as the
record holder or holders of such shares at such time and, at such time, all
interest on the Series A Junior Subordinated Debentures shall cease to accrue
and the rights of such Person or Persons as a Holder or Holders of Series A
Junior Subordinated Debentures shall cease.  Any Series A Junior Subordinated
Debentures surrendered for conversion shall be cancelled by the Trustee.

     (d) Definitions.  For the purpose of this Section 14, the failure of
holders of Series A Preferred Securities to receive, for 15 consecutive months,
the full amount of dividend payments (including arrearages and any Additional
Dividends (as defined in Section 1 of the Written Action)) on the Series A
Preferred Securities will constitute an "Exchange Event."  The term "Exchange
Election Date" shall mean the date of an Exchange Election Meeting (as defined
in Section 9(c) of the Written Action) at which the holders of a majority of the
aggregate liquidation preference of the Series A Preferred Securities authorize
the exchange of all the Series A Preferred Securities or, in the absence of such
meeting, the date of receipt by American General Delaware of a written consent
or consents signed by the holder or holders of a majority in aggregate
liquidation preference of the Series A Preferred Securities authorizing such
exchange.

                                       23
<PAGE>
 
     15.  CERTAIN PROVISIONS APPLICABLE TO CONVERSION INTO AMERICAN GENERAL
SERIES A PREFERRED STOCK.

     (a) Redemptions and Conversion.  Notwithstanding the provisions of Section
14, a Series A Junior Subordinated Debenture (or portion thereof) may not be
converted into American General Series A Preferred Stock if such Series A Junior
Subordinated Debenture (or applicable portion thereof) has been previously
surrendered for conversion into American General Common Stock or called for
redemption unless the applicable Redemption Price is not paid on the applicable
Redemption Date.

     (b) Consolidation, Mergers and Sale of Assets.  If the Company shall
consolidate with, or merge into, another Person or sell or transfer all or
substantially all of the property of the Company to another Person, in each case
prior to a conversion pursuant to Section 14, then, subject to the penultimate
sentence of this Section 15(b), lawful provision shall be made as part of the
terms of such transaction whereby each Holder of Series A Junior Subordinated
Debentures then Outstanding shall have the right thereafter to convert, at a
conversion rate as nearly equivalent as may be practicable to the rate specified
in Section 14, each such Series A Junior Subordinated Debenture upon the
occurrence of an Exchange Election only into shares of preferred stock of the
Person resulting from such consolidation, surviving such merger or to which such
property was transferred having substantially the same dividend and voting
rights, liquidation preference, and (subject to the provisions of Section 13)
other designations, preferences, limitations and relative rights as the American
General Series A Preferred Stock.  The Person resulting from such consolidation
or surviving such merger or which acquired such property, as the case may be,
shall make provision in its certificate or articles of incorporation or other
constituent document to establish such right.  The above provisions shall
similarly apply to successive transactions of the foregoing type.

     16.  CONVERSION AGENT.  Chemical Mellon Shareholder Services, LLC shall be
the initial Conversion Agent for the Series A Junior Subordinated Debentures.
Without in any way limiting any authority granted to the Conversion Agent under
the Written Action, in effecting the conversion and exchange transactions
described in Sections 11 and 14, the Conversion Agent is acting (i) in the case
of Sections 11(b) and 14, as agent of the holders of Series A Preferred
Securities, and (ii) in the case of Section 11(c), as agent for the Holders of
the Series A Junior Subordinated Debentures, directing it to effect such
conversion or exchange transactions.  Without in any way limiting any authority
granted to the Conversion Agent under the Written Action, the Conversion Agent
is authorized (i) to convert Series A Junior Subordinated Debentures into
American General Common Stock and thereupon to deliver such shares of American
General Common Stock, all in accordance with the provisions of Section 11, (ii)
to convert Series A Junior Subordinated Debentures following the occurrence of
an Exchange Event into American General Series A Preferred Stock and thereupon
to deliver such shares of American General Series A Preferred Stock, all in
accordance with the provisions of Section 14, and (iii) to conduct the other
activities specified herein to be performed by such Conversion Agent.  Subject
to the provisions of 601 of the Indenture, neither the Trustee nor the
Conversion Agent shall at any time be under any duty or responsibility to any
Holder of a Series A Junior

                                       24
<PAGE>
 
Subordinated Debenture or any holder of a Series A Preferred Security to
determine whether any facts exist which may require any adjustment of the
Conversion Price or any exchange contemplated hereby, or with respect to the
nature or extent of any such adjustment when made, or with respect to the method
employed in making the same.  Neither the Trustee nor the Conversion Agent shall
be accountable with respect to the validity or value (or the kind or amount) of
any shares of American General Common Stock, or of any securities or property or
cash, which may at any time be issued or delivered upon the conversion of any
Series A Junior Subordinated Debenture or upon any exchange contemplated hereby;
and neither the Trustee nor the Conversion Agent shall be deemed to make any
representation with respect thereto.  Subject to the provisions of 601 of the
Indenture, neither the Trustee nor the Conversion Agent shall be responsible for
any failure of the Company to issue, transfer or deliver any shares of American
General Common Stock or American General Series A Preferred Stock or stock
certificates or other securities or property or cash upon the surrender of any
Series A Junior Subordinated Debenture or Series A Preferred Security for the
purpose of conversion or exchange or to comply with any of the covenants of the
Company in this resolution, provided that the foregoing shall not relieve the
Conversion Agent of any responsibility it may have under this resolution to
deliver to the Person entitled to receive the same the shares of American
General Common Stock or American General Series A Preferred Stock or other
securities or property or cash which has been made available to the Conversion
Agent by the Company for such purpose.

     17.  RESERVATION OF SHARES; REGULATORY REQUIREMENTS; TAXES; LISTING.

     (a) Reservation of Shares.  The Company shall at all times reserve and keep
available out of its authorized and unissued American General Common Stock and
American General Series A Preferred Stock, solely for issuance upon the
conversion of the Series A Junior Subordinated Debentures, free from any
preemptive or other similar rights, such number of shares of American General
Common Stock and American General Series A Preferred Stock as shall from time to
time be issuable upon the conversion of all the Series A Junior Subordinated
Debentures then Outstanding.  Notwithstanding the foregoing, the Company shall
be entitled to deliver upon conversion of Series A Junior Subordinated
Debentures, shares of American General Common Stock or American General Series A
Preferred Stock, as appropriate, reacquired and held in the treasury of American
General (in lieu of the issuance of authorized and unissued shares), so long as
any such treasury shares are free and clear of all liens, charges, claims,
equities, security interests or encumbrances.  Any shares of American General
Common Stock or American General Series A Preferred Stock, as appropriate,
issued upon conversion of the Series A Junior Subordinated Debentures shall be
duly authorized, validly issued and fully paid and nonassessable.

     (b) Governmental Requirements.  The Company shall use its best efforts to
obtain and keep in force such governmental or regulatory permits or other
authorizations as may be required by law, and shall comply with all applicable
requirements as to registration or qualification of the American General Common
Stock and American General Series A Preferred Stock (and all requirements to
list on the applicable stock exchange, the American General Common Stock and
American General Series A Preferred Stock issuable upon

                                       25
<PAGE>
 
conversion of Series A Junior Subordinated Debentures that are at the time
applicable), that are necessary to enable the Company to lawfully issue American
General Common Stock and American General Series A Preferred Stock upon the
conversion of the Series A Junior Subordinated Debentures.

     (c) Taxes.  The Company shall pay any and all stock transfer and
documentary stamp taxes that may be payable in respect of the issuance or
delivery of shares of American General Common Stock or American General Series A
Preferred Stock, as the case may be, by the Company upon conversion of the
Series A Junior Subordinated Debentures.  The Company shall not, however, be
required to pay any tax, fee or governmental charge which may be payable in
respect of any transfer involved in the issuance or delivery of shares of
American General Common Stock or American General Series A Preferred Stock in a
name other than that in which the security so converted was registered and no
such issuance or delivery shall be made unless and until the Person requesting
such issuance or delivery has paid to the Conversion Agent the amount of any
such tax, fee or governmental charge or has established to the satisfaction of
the Conversion Agent that such tax, fee or governmental charge has been paid.
The Company and the Conversion Agent may require that such Person furnish a
suitable indemnity with respect to any tax, fee or other governmental charge
required to be paid with respect to such a transfer.  Nothing in this paragraph
(c) shall limit the requirement of the Company to withhold taxes pursuant to
applicable law or otherwise require the Company to pay any amounts on account of
such withholding.

     (d) Listing.  If the Series A Preferred Securities are listed on the NYSE
or another national securities exchange at the time of the distribution of the
Series A Junior Subordinated Debentures pursuant to a Series A Special Event
Exchange, then, prior to such distribution, the Company shall use its best
efforts to cause the Series A Junior Subordinated Debentures to be listed on the
NYSE or such other exchange on which the Series A Preferred Securities are then
listed.

     18.  CERTAIN PROVISIONS APPLICABLE AFTER A SERIES A SPECIAL EVENT EXCHANGE.
If, immediately prior to any Series A Special Event Exchange, the Series A
Preferred Securities are represented by one or more global securities held by
The Depository Trust Company ("DTC") or any successor securities depositary or
their respective nominees, then (a) DTC or such successor shall act as (and is
hereby appointed) the Depository for the Series A Junior Subordinated
Debentures, and (b) the Series A Junior Subordinated Debentures exchanged for
the Series A Preferred Securities upon such Series A Special Event Exchange
shall be represented by one or more global Series A Junior Subordinated
Debentures registered in the name of DTC or such successor securities depositary
or their respective nominees.

     After the date fixed for a Series A Special Event Exchange, any
certificates representing Series A Preferred Securities not held by DTC or any
successor securities depositary or their respective nominees and not surrendered
for exchange shall be deemed to represent Series A Junior Subordinated
Debentures having a principal amount and accrued and unpaid interest equal to
the liquidation preference plus accrued and unpaid

                                       26
<PAGE>
 
dividends (including Additional Dividends (as defined in Section 1 of the
Written Action)) of such Series A Preferred Securities until such certificates
are surrendered to the Conversion Agent for exchange in accordance with the
terms of the Series A Special Event Exchange.  Notwithstanding the foregoing,
until such certificates are so surrendered, no payments of interest or principal
will be made with respect to such Series A Junior Subordinated Debentures.

     19.  REGISTRAR.  The Series A Junior Subordinated Debentures may be
surrendered for registration of transfer or exchange and for conversion or
exchange at the Corporate Trust Office of the Trustee and any notices or demands
to or upon the Company in respect of the Series A Junior Subordinated Debentures
and the Indenture may be presented at that office.

     20.  FORM.  The certificates evidencing the Series A Junior Subordinated
Debentures shall be substantially in the form attached hereto as Annex A, with
such changes as the officer executing the same shall approve, such approval to
be evidenced by such officer's manual or facsimile signature.

     21.  TRANSFERABILITY.  Prior to a Series A Special Event Exchange, the
Series A Junior Subordinated Debentures may not be transferred by American
General Delaware without the Company's prior consent.  The Series A Junior
Subordinated Debentures may be distributed to the holders of the Series A
Preferred Securities upon the occurrence of a Tax Event or an Investment Company
Event (as such terms are defined in the Written Action) only upon the written
consent of the Company.

     22.  DENOMINATION.  The Series A Junior Subordinated Debentures shall be
issuable in denominations of $50 and any integral multiple thereof.

                                       27
<PAGE>
 
                                                                         ANNEX A



             FORM OF FACE OF SERIES A JUNIOR SUBORDINATED DEBENTURE

                          AMERICAN GENERAL CORPORATION

             6% Series A Convertible Junior Subordinated Debenture
                                    Due 2025


No. 1                                                              $313,291,100


          American General Corporation, a corporation duly organized and
existing under the laws of the State of Texas (herein called the "Company",
which term includes any successor under the Indenture referred to on the reverse
side), for value received, hereby promises to pay to American General Delaware,
L.L.C. or registered assigns, the principal sum of Three Hundred Thirteen
Million Two Hundred Ninety-One Thousand One Hundred ($313,291,100) Dollars on
the earlier of (i) May 31, 2025 or (ii) the date upon which American General
Delaware, L.L.C., a Delaware limited liability company (herein called "American
General Delaware"), is liquidated, dissolved or wound-up; provided, however,
that, if all the 6% Convertible Monthly Income Preferred Securities, Series A,
of American General Delaware (herein called the "Series A Preferred Securities")
are exchanged (herein called a "Series A Special Event Exchange") for Series A
Junior Subordinated Debentures (as defined on the reverse side) in accordance
with the terms of the Series A Preferred Securities, this Series A Junior
Subordinated Debenture will mature on May 31, 2025, notwithstanding that
American General Delaware may have liquidated, dissolved or wound-up in
connection with or after such Series A Special Event Exchange.  The Company also
agrees to pay interest on the principal hereof at the rate of 6% per annum from
June 1, 1995 (or from the most recent Interest Payment Date, as hereinafter
defined, to which interest has been paid or duly provided for), payable monthly
in arrears on the last day of each calendar month of each year (each an
"Interest Payment Date"), commencing June 30, 1995, until the principal hereof
is paid or made available for payment.  To the fullest extent permitted by
applicable law, interest will accrue at the rate of 6% per annum on any interest
installment that is not paid at the end of any monthly interest period
compounded monthly (herein, together with the Additional Amounts referred to in
the Indenture, called "Additional Interest").  The amount of interest payable
for any period shall be computed on the basis of a 360 day year consisting of
twelve 30-day months and, for any period shorter than a full monthly interest
payment period, will be computed on the basis of the actual number of days
elapsed in such period.  If any date on which interest is payable on this Series
A Junior Subordinated Debenture is not a Business Day, then the payment of the
interest payable on such date will be made on the next succeeding day which is a
Business Day (and without any interest or other payment in respect of any such
delay), except that, if such Business Day is in the next succeeding calendar
year, such payment shall

                                       28
<PAGE>
 
be made on the immediately preceding Business Day, in each case with the same
force and effect as if made on such date.  A "Business Day" shall mean any day
other than a Saturday, Sunday or other day on which banking institutions in New
York City are authorized or obligated by law or executive order to close.  The
interest so payable, and punctually paid or duly provided for, on any Interest
Payment Date will, as provided in the Indenture, be paid to the Person in whose
name this Series A Junior Subordinated Debenture (or one or more Predecessor
Securities, as defined in the Indenture) is registered at the close of business
on the Regular Record Date for such Interest Payment Date.  The Regular Record
Date shall be the Business Day next preceding such Interest Payment Date,
provided that if the Series A Junior Subordinated Debentures are not in book-
entry-only form during any period following a Series A Special Event Exchange,
the Regular Record Date for any Interest Payment Date within such period shall
be the 15th day of the month in which such Interest Payment Date occurs.  Any
such interest not so punctually paid or duly provided for (other than by reason
of the following paragraph) will forthwith cease to be payable to the Holder on
such Regular Record Date and may either be paid to the Person in whose name this
Series A Junior Subordinated Debenture (or one or more Predecessor Securities)
is registered at the close of business on a Special Record Date for the payment
of such Defaulted Interest to be fixed by the Trustee, or be paid at any time in
any other lawful manner not inconsistent with the requirements of any securities
exchange on which the Securities may be listed, and upon such notice as may be
required by such exchange, all as more fully provided in such Indenture.

          The Company shall have the right, at any time and from time to time,
to extend the interest payment period hereof to a period ending on the last day
of a calendar month (herein called an "Extension Period") not exceeding 60
consecutive months, but in no event beyond the date of Stated Maturity or the
Redemption Date of this Series A Junior Subordinated Debenture.  During an
Extension Period, interest will continue to accrue and compound monthly.  Prior
to the termination of any Extension Period of less than 60 consecutive months,
the Company may further extend the interest payment period hereof, provided that
such Extension Period may not exceed 60 consecutive months and may not extend
beyond the date of Stated Maturity or the Redemption Date of this Series A
Junior Subordinated Debenture.  Upon the termination of any Extension Period and
the payment of all accrued and unpaid interest (including any Additional
Interest) then due, the Company may select a new Extension Period, subject to
the above requirements.  No interest shall be due during an Extension Period
until the end of such period.  Such interest shall be due and payable on the
Interest Payment Date which is the last day of the Extension Period to the
Person in whose name this Series A Junior Subordinated Debenture is registered
on the Regular Record Date for such Interest Payment Date.

          Payment of the principal of and interest on this Series A Junior
Subordinated Debenture will be made at the office or agency of the Company
maintained for that purpose in New York, New York, in such coin or currency of
the United States of America as at the time of payment is legal tender for
payment of public and private debts; provided, however, that at the option of
the Company payment of interest may be made (i) by check mailed to the address
of the Person entitled thereto as such address shall appear in the Security
Register or (ii) subject to the procedures of the Paying Agent, by wire transfer
in

                                       29
<PAGE>
 
immediately available funds at such place and to such account at a bank located
in the United States as may be designated by the Person entitled thereto as
specified in the Security Register.

          Reference is hereby made to the further provisions of the Indenture
summarized on the reverse hereof, which further provisions shall for all
purposes have the same effect as if set forth at this place.

          Unless the certificate of authentication hereon has been executed by
the Trustee referred to on the reverse hereof by manual signature, this Series A
Junior Subordinated Debenture shall not be entitled to any benefit under the
Indenture or be valid or obligatory for any purpose.

          IN WITNESS WHEREOF, the Company has caused this instrument to be duly
executed under its corporate seal.

Dated:


                                                  AMERICAN GENERAL CORPORATION



                                                  By:__________________________
                                                     Name:
                                                     Title:


[SEAL]


Attest:_______________________


                    TRUSTEE'S CERTIFICATE OF AUTHENTICATION

          This is one of the Securities of the series designated herein referred
to in the within-mentioned Indenture.

                                                    CHEMICAL BANK

                                                    As Trustee


                                                    By ________________________
                                                          Authorized Officer

                                       30
<PAGE>
 
           FORM OF REVERSE OF SERIES A JUNIOR SUBORDINATED DEBENTURE

     This Series A Junior Subordinated Debenture is one of a duly authorized
issue of Securities of the Company, designated as its 6% Series A Convertible
Junior Subordinated Debentures due 2025 (herein called the "Series A Junior
Subordinated Debentures"), limited in aggregate principal amount to $281,962,050
(or up to 313,291,100 aggregate principal amount if and to the extent the over-
allotment option granted to the underwriters for the sale of the Series A
Preferred Securities is exercised), issued and to be issued under an Indenture,
dated as of May 15, 1995 (herein called the "Indenture"), between the Company
and Chemical Bank, as Trustee (herein called the "Trustee", which term includes
any successor trustee under the Indenture).  Reference is made to the Indenture
and all indentures supplemental thereto (including the Board Resolution setting
forth the terms of this series of Securities) for a statement of the respective
rights, limitations of rights, duties and immunities thereunder of the Company,
the Trustee, the holders of Senior Indebtedness and the Holders of the Series A
Junior Subordinated Debentures and other series of Securities which may be
issued pursuant to the Indenture and of the terms upon which the Securities are,
and are to be, authenticated and delivered.  All terms used in this Series A
Junior Subordinated Debenture which are defined in the Indenture shall have the
meanings assigned to them in the Indenture.

     The indebtedness evidenced by this Series A Junior Subordinated Debenture,
including all principal and interest (including Additional Interest), is, to the
extent provided in the Indenture, subordinate and subject in right of payment to
the prior payment in full of all Senior Indebtedness, and this Series A Junior
Subordinated Debenture is issued subject to the provisions of the Indenture with
respect thereto.  The Holder of this Series A Junior Subordinated Debenture, by
accepting the same, (a) agrees to and shall be bound by such provisions, (b)
authorizes and directs the Trustee on his behalf to take such action as may be
necessary or appropriate to effectuate the subordination so provided and (c)
appoints the Trustee his attorney-in-fact for any and all such purposes.

     If an Event of Default with respect to the Series A Junior Subordinated
Debentures shall occur and be continuing, the principal of the Series A Junior
Subordinated Debentures may be declared due and payable in the manner and with
the effect provided in the Indenture.

     The Indenture permits, with certain exceptions as therein provided, the
amendment thereof and the modification of the rights and obligations of the
Company and the rights of the Holders of the Series A Junior Subordinated
Debentures under the Indenture at any time by the Company and the Trustee with,
in some cases, the consent of the Holders of a majority in aggregate principal
amount of the Series A Junior Subordinated Debentures at the time Outstanding
and, in other cases, without the consent of any Holders.  The Indenture also
contains provisions permitting the Holders of specified percentages in principal
amount of the Series A Junior Subordinated Debentures, on behalf of the Holders
of all Series A Junior Subordinated Debentures, to waive compliance by the
Company with certain provisions of the Indenture and certain past defaults under
the Indenture and their consequences.  Any such consent or waiver shall be
conclusive and binding upon the Holder

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<PAGE>
 
of this Series A Junior Subordinated Debenture and upon all future Holders of
this Series A Junior Subordinated Debenture and of any Series A Junior
Subordinated Debenture issued upon the registration of transfer hereof or in
exchange herefor or in lieu hereof, whether or not notation of such consent is
made upon this Series A Junior Subordinated Debenture or thereon.

     Subject to and in compliance with the provisions of the Indenture, this
Series A Junior Subordinated Debenture is convertible at any time on or before
the earlier of close of business on the Conversion Expiration Date or Conversion
Expiration Date of the Series A Junior Subordinated Debentures at the option of
the Holder hereof into fully paid and nonassessable shares of American General
Common Stock at an initial conversion price of $40.69 principal amount hereof
per share of American General Common Stock, subject to adjustment as provided
for in the Indenture.  Notwithstanding the conversion hereof after a Regular
Record Date but before the corresponding Interest Payment Date, the Holder
hereof will be entitled to receive the interest payable on this Series A Junior
Subordinated Debenture on such next succeeding Interest Payment Date.  No other
adjustment, however, shall be made for accrued interest, including Additional
Interest, whether or not in arrears.  No fractional shares of American General
Common Stock will be issued as a result of conversion, but in lieu thereof such
fractional interest will be paid in cash by the Company.  On or after May 31,
2000, the Company may, at its option, cause the conversion rights of Holders of
Series A Junior Subordinated Debentures to expire if (i) the Company is then
current in the payment of interest (without regard to any Extension Period) on
the Series A Junior Subordinated Debentures and (ii) for 20 Trading Days within
any period of 30 consecutive Trading Days, including the last Trading Day of
such period, the Current Market Price of American General Common Stock shall
have exceeded 120% of the Conversion Price then in effect.

     If at any time following the Conversion Expiration Date or Conversion
Expiration Date of the Series A Junior Subordinated Debentures, less than 10% of
the aggregate principal amount of the Series A Junior Subordinated Debentures
originally purchased by American General Delaware with the proceeds from the
sale of the Series A Preferred Securities remains Outstanding, then such Series
A Junior Subordinated Debentures shall be subject to redemption, in whole but
not in part, at the option of the Company upon not less than 30 days' nor more
than 60 days' notice, at a cash Redemption Price equal to the unpaid principal
amount thereof, without premium or penalty, plus any accrued and unpaid interest
(including any Additional Interest) thereon to the Redemption Date.

     The Series A Junior Subordinated Debentures are also subject to redemption,
at the option of the Company, in whole or in part, at any time or from time to
time on or after May 31, 2003, at a cash Redemption Price equal to the unpaid
principal amount thereof, without premium or penalty, plus any accrued and
unpaid interest (including any Additional Interest) thereon to the Redemption
Date.  If American General Delaware redeems the Series A Preferred Securities in
accordance with the terms thereof, the Series A Junior Subordinated Debentures
shall be due and payable and shall be redeemed by the Company in an aggregate
principal amount equal to the aggregate stated liquidation preference of the
Series A Preferred Securities so redeemed at a Redemption Price equal to the
unpaid

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<PAGE>
 
principal amount of the Series A Junior Subordinated Debentures so redeemed,
without premium or penalty, plus any accrued and unpaid interest (including any
Additional Interest) thereon to the Redemption Date.

     In addition, if the Company or any of its Subsidiaries acquires any Series
A Preferred Securities by tender, in the open market or otherwise, the Company
shall have the right to redeem the Series A Junior Subordinated Debentures, in
an aggregate principal amount not to exceed the aggregate stated liquidation
preference of the Series A Preferred Securities so purchased, at a cash
Redemption Price equal to the principal amount thereof, without premium or
penalty, plus any accrued and unpaid interest (including any Additional
Interest) thereon to the Redemption Date.

     Upon the occurrence of an Exchange Event, the Series A Junior Subordinated
Debentures are convertible into Series A Cumulative Convertible Preferred Stock
of the Company as provided under the terms of the Indenture.

     As provided in the Indenture and subject to certain limitations set forth
therein, the transfer of this Series A Junior Subordinated Debenture is
registrable in the Security Register, upon surrender of this Series A Junior
Subordinated Debenture for registration of transfer at the office or agency of
the Trustee in New York City, duly endorsed by, or accompanied by a written
instrument of transfer in form satisfactory to the Company and the Security
Registrar duly executed by, the Holder hereof or his attorney duly authorized in
writing, and thereupon one or more new Series A Junior Subordinated Debentures,
of authorized denominations and for the same aggregate principal amount, will be
issued to the designated transferee or transferees; provided, however, that,
prior to a Series A Special Event Exchange, this Series A Junior Subordinated
Debenture may not be transferred without the written consent of the Company.

     The Series A Junior Subordinated Debentures are issuable only in registered
form without coupons in denominations of $50 and any integral multiple thereof.
As provided in the Indenture and subject to certain limitations set forth
therein, Series A Junior Subordinated Debentures are exchangeable for a like
aggregate principal amount of Series A Junior Subordinated Debentures of a
different authorized denomination, as requested by the Holder surrendering the
same.

     No service charge shall be made for any such registration of transfer or
exchange, but the Company may require payment of a sum sufficient to cover any
tax or other governmental charge payable in connection therewith.

     Prior to due presentment of this Series A Junior Subordinated Debenture for
registration of transfer, the Company, the Trustee and any agent of the Company
or the Trustee may treat the Person in whose name this Series A Junior
Subordinated Debenture is registered as the owner hereof for all purposes,
whether or not this Series A Junior Subordinated Debenture be overdue, and
neither the Company, the Trustee nor any such agent shall be affected by notice
to the contrary.

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<PAGE>
 
     No recourse shall be had for the payment of the principal of or interest
(including Additional Interest, if any) on this Series A Junior Subordinated
Debenture, or for any claim based hereon, or otherwise in respect hereof, or
based on or in respect of the Indenture or any indenture supplemental thereto,
against any incorporator, stockholder, officer or director, as such, past,
present or future, of the Company or of any successor corporation, all such
liability being, by the acceptance hereof and as part of the consideration for
the issue hereof, expressly waived and released.

                                       34