<PAGE>

                                                                    EXHIBIT 4(j)

     THIS GUARANTEE AGREEMENT (this "Guarantee"), dated as of May 24, 1995, is
executed and delivered by American General Corporation, a corporation organized
under the laws of the State of Texas ("American General"), for the benefit of
the Holders (as hereinafter defined) from time to time of the Preferred
Securities (as hereinafter defined) of American General Delaware, L.L.C., a
Delaware limited liability company ("American General Delaware").

     WHEREAS, American General Delaware intends to issue and sell from time to
time, in one or more series, preferred limited liability company interests (the
"Preferred Securities"), and American General desires to issue this Guarantee
for the benefit of the Holders of the Preferred Securities, as provided herein;

     WHEREAS, American General Delaware will purchase the Junior Subordinated
Debentures (as hereinafter defined) issued pursuant to the Junior Subordinated
Indenture (as hereinafter defined) with substantially all of the proceeds from
the issuance and sale of the Preferred Securities and its other common limited
liability company interests (the "Common Securities"); and

     WHEREAS, American General desires hereby to unconditionally and irrevocably
guarantee, to the extent set forth herein, the payment in full to the Holders of
the Guarantee Payments (as hereinafter defined) and the performance of the other
obligations set forth herein.

     NOW, THEREFORE, in consideration of the purchase by each Holder of the
Preferred Securities, which purchase American General hereby agrees shall
benefit American General, American General executes and delivers this Guarantee
for the benefit of the Holders.

                                   ARTICLE I

                                  DEFINITIONS

     As used in this Guarantee, the terms set forth below shall, unless the
context otherwise requires, have the following meanings.  Capitalized terms used
herein but not otherwise defined herein shall have the meanings ascribed to such
terms in the Amended and Restated Limited Liability Company Agreement of
American General Delaware, L.L.C., dated as of May 24, 1995 (the "LLC
Agreement").

     1.1  "Additional Dividends" shall mean Dividends (as hereinafter defined)
that shall be declared and paid by American General Delaware on any Dividend
arrearages in respect of the Preferred Securities of any series at the rate set
forth in the Declaration (as hereinafter defined) with respect to such series of
Preferred Securities.
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     1.2  "American General Common Stock" shall mean the Common Stock, par value
$.50 per share, of American General.  However, subject to the anti-dilution
provisions of the applicable series of Junior Subordinated Debentures (as
hereinafter defined), shares of American General Common Stock issuable on
conversion of such Junior Subordinated Debentures or upon exchange of the
American General Preferred Stock (as hereinafter defined) shall include only
shares of the class designated as Common Stock of American General on the date
hereof or shares of any class or classes resulting from any reclassification or
reclassifications thereof and which have no preference as to the payment of
dividends or the distribution of assets upon any voluntary or involuntary
liquidation, dissolution or winding-up of American General and which are not
subject to redemption by American General; provided, that if at any time there
shall be more than one such resulting class, the shares of each such class then
so issuable shall be substantially in the proportion which the total number of
shares of such class resulting from all such reclassification bears to the total
number of shares of all such classes resulting from all such reclassification.

     1.3  "American General Preferred Stock" shall mean the series, if any, of
Preferred Stock, par value $1.50 per share, of American General exchangeable for
the related series of Junior Subordinated Debentures.

     1.4  "Conversion Agent" shall mean Chemical Mellon Shareholder Services,
LLC and its successors (or such substitute entity as may be designated from time
to time by the Manager (as hereinafter defined), acting as agent of the Holders
in effecting, as applicable, (a) the exchange of the Preferred Securities of any
series into the related series of Junior Subordinated Debentures and the
conversion of such Junior Subordinated Debentures into shares of American
General Common Stock or (b) the exchange of Preferred Securities of any series
for the related series of Junior Subordinated Debentures and the conversion of
such Junior Subordinated Debentures for the related series of American General
Preferred Stock, in each case as and in such manner as may be set forth in the
LLC Agreement and the Declaration with respect to such series of Preferred
Securities.

     1.5  "Declaration" shall mean, with respect to any series of Preferred
Securities, the Written Action adopted by the Manager pursuant to Section 7.1(b)
of the LLC Agreement relating to such series of Preferred Securities.

     1.6  "Dividends" shall mean, with respect to any series of Preferred
Securities, the cumulative cash distributions from American General Delaware
with respect to such series of Preferred Securities, accruing and payable in the
manner set forth in the Declaration with respect to such series of Preferred
Securities.

     1.7  "Guarantee Payments" shall mean, with respect to any series of
Preferred Securities, the following payments, without duplication, to the extent
not paid by American General Delaware:  (a) any accumulated and unpaid Dividends
(whether or not earned), including any Additional Dividends, which are required
to be paid on such Preferred Securities, but only if and to the extent that such
Dividends have been declared on such Preferred Securities from funds of American
General Delaware legally available therefor; (b) the Redemption Price (including
all accumulated and unpaid Dividends (whether or not

                                       2
<PAGE>
 
earned or declared), including any Additional Dividends) payable with respect to
any such Preferred Securities called for redemption by American General
Delaware, but only to the extent payable out of funds of American General
Delaware legally available therefor; and (c) upon the voluntary or involuntary
liquidation, dissolution or winding-up of American General Delaware other than
in connection with or after the exchange, if applicable, of such Preferred
Securities for the related series of Junior Subordinated Debentures, the lesser
of (i) the Liquidation Distribution and (ii) the amount of assets of American
General Delaware available for distribution to Holders of such Preferred
Securities in liquidation, dissolution or winding-up of American General
Delaware.

     1.8  "Holder" shall mean the registered holder from time to time of any
Preferred Securities of American General Delaware; provided, however, that in
determining whether the Holders of the requisite percentage of Preferred
Securities have given any request, notice, consent or waiver hereunder, "Holder"
shall not include American General or any majority-owned entity thereof, either
directly or indirectly.

     1.9  "Junior Subordinated Debentures" shall mean the series of Junior
Subordinated Debentures issued by American General pursuant to the Junior
Subordinated Indenture and delivered to American General Delaware in connection
with the issuance and sale by American General Delaware of the related series of
Preferred Securities.  The Junior Subordinated Debentures will evidence the loan
made by American General Delaware to American General of substantially all of
the proceeds received by American General Delaware from the issuance and sale of
the related series of Preferred Securities and the Common Securities.

     1.10  "Junior Subordinated Indenture" shall mean the Indenture, dated as of
May 15, 1995, between American General and Chemical Bank, as Trustee.

     1.11  "Manager" means American General Delaware Management Corporation, in
its capacity as the manager of American General Delaware, or any permitted
successor manager of American General Delaware admitted as such pursuant to the
applicable provisions of the LLC Agreement.

     1.12  "Redemption Price" shall mean, with respect to any series of
Preferred Securities subject to redemption by American General Delaware, the
liquidation preference of such Preferred Securities plus accumulated and unpaid
dividends (whether or not earned or declared), including any Additional
Dividends, to the date fixed for redemption thereof.

     1.13  "Special Trustee" shall mean, with respect to any series of Preferred
Securities, a special trustee appointed by the Holders of the Preferred
Securities of such series pursuant to Section 8.1 of the LLC Agreement and
authorized, among other things, to enforce American General Delaware's rights
under the related series of Junior Subordinated Debentures against American
General and to enforce the obligations undertaken with respect to such series of
Preferred Securities by American General under this Guarantee.

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<PAGE>
 
                                  ARTICLE II

                                   GUARANTEE

          2.1  GENERAL.  American General irrevocably and unconditionally agrees
to pay in full to the Holders of each series of Preferred Securities the
Guarantee Payments with respect to such series of Preferred Securities, as and
when due (except to the extent previously paid by American General Delaware),
regardless of any defense, right of set-off or counterclaim which American
General Delaware may have or assert.  American General's obligation to make a
Guarantee Payment may be satisfied by direct payment of the required amounts by
American General to the Holders of such series of Preferred Securities or by
causing American General Delaware to pay such amounts to such Holders.

          2.2  WAIVER OF CERTAIN RIGHTS.  American General hereby waives, to the
fullest extent permitted by applicable law, notice of acceptance of this
Guarantee and of any liability to which it applies or may apply, presentment,
demand for payment, protest, notice of nonpayment, notice of dishonor, notice of
redemption and all other notices and demands.

          2.3  OBLIGATIONS NOT AFFECTED.  The obligations, covenants, agreements
and duties of American General under this Guarantee shall in no way be affected
or impaired by reason of the happening from time to time of any of the
following:

          (a) the release or waiver, by operation of law or otherwise, of the
     performance or observance by American General Delaware of any express or
     implied agreement, covenant, term or condition relating to the Preferred
     Securities of any series to be performed or observed by American General
     Delaware;

          (b) the extension of time for the payment by American General Delaware
     of all or any portion of the Dividends, Additional Dividends, Redemption
     Price, Liquidation Distribution or any other sums payable under the terms
     of the Preferred Securities of any series or the extension of time for the
     performance of any other obligation under, arising out of, or in connection
     with, the Preferred Securities of such series;

          (c) any failure, omission, delay or lack of diligence on the part of
     the Holders of Preferred Securities of any series or the Special Trustee to
     enforce, assert or exercise any right, privilege, power or remedy conferred
     on such Holders or such Special Trustee pursuant to the terms of the
     Preferred Securities of such series, or any action on the part of American
     General Delaware granting indulgence or extension of any kind;

          (d) the voluntary or involuntary liquidation, dissolution, winding-up,
     sale of any collateral, receivership, insolvency, bankruptcy, assignment
     for the benefit of creditors, reorganization, arrangement, composition or
     readjustment of debt of, or other similar proceedings affecting, American
     General Delaware or any of the assets of American General Delaware;

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<PAGE>
 
          (e) any invalidity of, or defect or deficiency in, any of the
     Preferred Securities of any series;

          (f) the settlement or compromise of any obligation guaranteed hereby
     or hereby incurred; or

          (g) to the fullest extent permitted by applicable law, any other
     circumstance whatsoever that might otherwise constitute a legal or
     equitable discharge or defense of a guarantor, it being the intent of this
     Section 2.3 that the obligations of American General hereunder shall be
     absolute and unconditional under any and all circumstances.

There shall be no obligation of any Holders of Preferred Securities to give
notice to, or obtain any consent of, American General with respect to the
happening of any of the foregoing.

     2.4  PROCEEDING DIRECTLY AGAINST AMERICAN GENERAL.  This Guarantee is a
guarantee of payment and not of collection.  A Holder of Preferred Securities of
any series or the Special Trustee may enforce this Guarantee with respect to
such series of Preferred Securities directly against American General, and
American General waives any right or remedy to require that any action be
brought against American General Delaware or any other person or entity before
proceeding against American General.  Subject to Section 2.5 hereof, all waivers
herein contained shall be without prejudice to the right of a Holder or the
Special Trustee, at its option, to proceed against American General Delaware,
whether by separate action or by joinder.  American General agrees that this
Guarantee shall not be discharged except by payment of the Guarantee Payments in
full (to the extent not previously paid by American General Delaware) and by
complete performance of all obligations under this Guarantee.

     2.5  SUBROGATION.  American General shall be subrogated to all (if any)
rights of the Holders of Preferred Securities against American General Delaware
in respect of any amounts paid to such Holders by American General under this
Guarantee and shall have the right to waive payment by American General Delaware
of any amount of Dividends in respect of which payment has been made to the
Holders by it pursuant to Section 2.1 hereof; provided, however, that American
General shall not (except to the extent required by mandatory provisions of law)
exercise any rights which it may acquire by way of subrogation or any indemnity,
reimbursement or other agreement, in all cases as a result of a payment under
this Guarantee, if, at the time of any such payment, any amounts are due and
unpaid under this Guarantee.  If any amount shall be paid to American General in
violation of the preceding sentence, American General agrees to hold such amount
in trust for the Holders and to pay over such amount promptly to the Holders.

     2.6  INDEPENDENT OBLIGATIONS.  American General acknowledges that its
obligations hereunder are independent of the obligations of American General
Delaware with respect to the Preferred Securities and that American General
shall be liable as principal and sole debtor under this Guarantee to make
Guarantee Payments in full pursuant to the terms of

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this Guarantee notwithstanding the occurrence of any event referred to in
subsections (a) through (g), inclusive, of Section 2.3 hereof.

     2.7  TERMINATION.  This Guarantee shall terminate and be of no further
force and effect as to the Preferred Securities of any series upon (a) full
payment of the Redemption Price of all outstanding Preferred Securities of such
series, (b) if applicable, the exchange (in the manner provided in the LLC
Agreement and the applicable Declaration) of all of the Preferred Securities of
such series for the Junior Subordinated Debentures of the related series and the
conversion (in the manner provided in the Junior Subordinated Indenture) of such
Junior Subordinated Debentures for American General Common Stock or the series
of American General Preferred Stock related to such series of Preferred
Securities, as the case may be, or (c) if applicable, the exchange (in the
manner provided in the LLC Agreement or such Declaration) of all of the
Preferred Securities of such series for the Junior Subordinated Debentures of
the related series.  In addition, this Guarantee will terminate completely upon
full payment of the aggregate Liquidation Distributions applicable to all
outstanding series of Preferred Securities.  Notwithstanding the foregoing, this
Guarantee shall continue to be effective or, to the fullest extent permitted by
applicable law, shall be reinstated, as the case may be, with respect to the
Preferred Securities of any series if at any time any Holder of such Preferred
Securities must restore payment of any sums recovered on account of, or must
redeliver any securities received on account of, such Preferred Securities or
under this Guarantee for any reason whatsoever.

                                  ARTICLE III

                     CERTAIN COVENANTS OF AMERICAN GENERAL

     3.1  DIVIDENDS AND OTHER PAYMENTS.  So long as the Preferred Securities of
any series remain outstanding, American General will not declare or pay any
dividend on, and American General will not, and American General will not permit
any of its majority-owned subsidiaries to, redeem, purchase, acquire or make a
liquidation payment with respect to, any of American General's capital stock
(other than (i) purchases or acquisitions of shares of American General Common
Stock in connection with the satisfaction by American General or any of its
majority-owned subsidiaries of its obligations under any employee benefit plans
or the satisfaction by American General of its obligations pursuant to any put
contract requiring American General to purchase any American General Common
Stock, (ii) as a result of a reclassification of American General's capital
stock or the exchange or conversion of one class or series of American General's
capital stock for another class or series of American General's capital stock,
(iii) redemptions or purchases of any share purchase rights issued by American
General pursuant to the Rights Agreement dated as of July 27, 1989, as amended
from time to time, or the declaration and payment of a dividend or distribution
of similar share purchase rights in the future or (iv) the purchase of
fractional interests in shares of American General's capital stock pursuant to
the conversion or exchange provisions of such American General capital stock or
the security being converted or exchanged) or make any guarantee payments with
respect to the foregoing, if at such time American General has exercised its
option to extend an interest payment period on the series of Junior Subordinated
Debentures related to such series of Preferred

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Securities and such extension is continuing, American General is in default with
respect to its payment or other obligations hereunder or there has occurred and
is continuing any Event of Default (as defined in the Junior Subordinated
Indenture) with respect to the series of Junior Subordinated Debentures related
to such series of Preferred Securities.  American General shall take all actions
necessary to ensure the compliance of its majority-owned subsidiaries with this
Section 3.1.

     3.2  CERTAIN OTHER COVENANTS.  So long as the Preferred Securities of any
series remain outstanding, American General shall:  (a) not cause or permit any
Common Securities to be transferred (other than, in the case of American
General, in connection with a merger or consolidation permitted under the Junior
Subordinated Indenture or, in the case of the Manager, in connection with any
merger or consolidation involving the Manager), (b) maintain direct or indirect
ownership of all outstanding Common Securities and any other limited liability
company interests in American General Delaware other than any series of
Preferred Securities (except as may be permitted in the LLC Agreement); (c)
cause at least 21% of all interests in the capital, income, gain, loss,
deduction and credit of American General Delaware to be represented by Common
Securities; (d) not voluntarily liquidate, dissolve or wind-up itself (other
than in connection with a merger or consolidation permitted under the Junior
Subordinated Indenture), or permit the Manager (other than in connection with
any merger or consolidation involving the Manager) or American General Delaware
(other than in connection with or after an exchange of all outstanding series of
Preferred Securities for the related series of Junior Subordinated Debentures,
if so provided in the Declaration relating to each such series of Preferred
Securities) to liquidate, dissolve or wind-up; (e) cause American General
Delaware Management Corporation or any successor thereto by merger or
consolidation to remain the Manager and to timely perform all of its duties as
Manager (including the duty to cause American General Delaware to declare and
pay dividends on all outstanding series of Preferred Securities to the extent
set forth in the LLC Agreement and the applicable Declaration); and (f) subject
to the terms of the Preferred Securities of any series, use reasonable efforts
to cause American General Delaware to remain a Delaware limited liability
company and otherwise continue to be treated as a partnership for United States
federal income tax purposes.


                                   ARTICLE IV

                                     STATUS

     4.1  STATUS.  American General covenants and agrees that this Guarantee
constitutes an unsecured obligation of American General ranking (i) subordinate
and junior in right of payment to all other liabilities of American General
other than the guarantees referred to in clauses (ii) and (iii) of this Section
4.1, (ii) pari passu with the most senior preferred stock issued by American
General, with that Guarantee dated as of May 24, 1995 in respect of certain
securities issued by American General Capital, L.L.C. and with any other
guarantee executed by American General in respect of any preferred stock or
interest of any affiliate of American General that provides that such guarantee
is pari passu in right of payment with this Guarantee and (iii) senior to
American General Common Stock, any

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other class or series of capital stock issued by American General which by its
express terms ranks junior to the most senior preferred stock issued by American
General as to the payment of dividends and the distribution of assets upon the
liquidation, dissolution or winding-up of American General and any guarantee
executed by American General that provides that such guarantee is junior in
right of payment to this Guarantee.

                                   ARTICLE V

                CONVERSION AND EXCHANGE OF PREFERRED SECURITIES

     5.1  ISSUANCE OF AMERICAN GENERAL COMMON STOCK.  If the Preferred
Securities of any series are convertible into shares of American General Common
Stock pursuant to the applicable Declaration, American General hereby agrees
that, upon the request of the Conversion Agent (on behalf of one or more Holders
of such Preferred Securities), to convert Junior Subordinated Debentures of the
series related to such series of Preferred Securities into American General
Common Stock pursuant to the request of such Holders to effect such conversion
in accordance with the terms of the LLC Agreement and such Declaration, American
General shall deliver to the Conversion Agent certificates representing the
number of full shares of American General Common Stock issuable upon conversion
of such Junior Subordinated Debentures in accordance with the terms of the
Junior Subordinated Indenture and such Junior Subordinated Debentures.  American
General shall reserve and keep available out of its authorized and unissued
American General Common Stock (solely for issuance upon the conversion of such
Junior  Subordinated Debentures), free of any preemptive or other similar
rights, the number of full shares of American General Common Stock deliverable
by the Conversion Agent to the Holders upon the conversion of all outstanding
convertible Preferred Securities not theretofore converted by the Holders.

     5.2  VALIDITY OF AMERICAN GENERAL COMMON STOCK.  All shares of American
General Common Stock delivered by American General upon such conversion will be
duly authorized, validly issued and fully paid and nonassessable.

     5.3  ISSUANCE OF AMERICAN GENERAL PREFERRED STOCK.  American General hereby
agrees, upon the making of an Exchange Election (as such term may be defined in
the applicable Declaration) by the Holders of a majority of the aggregate
liquidation preference of the outstanding Preferred Securities of the related
series in accordance with the terms of the LLC Agreement and such Declaration,
to issue one share of American General Preferred Stock of the related series in
respect of the applicable principal amount (as set forth in such Declaration) of
Junior Subordinated Debentures of the related series.  American General further
agrees, upon receipt of a Notice of Exchange Election (as defined in such
Declaration), to deliver to the Conversion Agent the number of shares of
American General Preferred Stock of the related series issuable upon conversion
of such Junior Subordinated Debentures.  American General shall reserve and keep
available out of its authorized and unissued American General Preferred Stock
(solely for issuance upon conversion of such Junior Subordinated Debentures),
free of any preemptive or other similar rights, the number of shares of American
General Preferred Stock of the related

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series deliverable by the Conversion Agent to the Holders upon exchange of all
outstanding exchangeable Preferred Securities.

     5.4  VALIDITY OF AMERICAN GENERAL PREFERRED STOCK.  All such shares of
American General Preferred Stock issued by American General upon such conversion
will be duly authorized, validly issued and fully paid and nonassessable.

     5.5  TERMINATION OF OBLIGATION TO ISSUE AMERICAN GENERAL COMMON STOCK.
American General's obligations under this Article V to issue American General
Common Stock shall terminate upon the termination of the right of Holders of
Preferred Securities to request the Conversion Agent to effect such conversion
as may be set forth in the LLC Agreement and any applicable Declaration.

                                   ARTICLE VI

                                 MISCELLANEOUS

     6.1  THIRD PARTY BENEFICIARIES.  All of American General's obligations
under this Guarantee shall be directly enforceable by the Holders from time to
time of the applicable series of Preferred Securities.  Each Holder of Preferred
Securities of the applicable series is an intended third-party beneficiary of
this Guarantee.

     6.2  SUCCESSORS AND ASSIGNS.  All provisions contained in this Guarantee
shall bind the successors, assigns, receivers, trustees and representatives of
American General and shall inure to the benefit of the Holders.  Except as
permitted by Section 6.4, American General shall not assign its rights or
delegate its obligations hereunder without the prior approval (obtained in the
manner set forth in the LLC Agreement) of the Holders of not less than 66-2/3%
of the aggregate liquidation preference of all Preferred Securities of all
series then outstanding voting as a single class.

     6.3  AMENDMENTS.  Except with respect to any changes which do not adversely
affect the rights of any Holders of Preferred Securities (in any of which cases
no vote will be required), this Guarantee may be amended with respect to the
Preferred Securities of any series affected by such amendment only with the
prior approval (obtained in the manner set forth in the LLC Agreement and the
applicable Declaration) of the Holders of not less than 66-2/3% of the aggregate
liquidation preference of the outstanding Preferred Securities of such series.

     6.4  MERGER OR CONSOLIDATION.  American General may consolidate with or
merge with or into any other person or entity, provided that such consolidation
or merger is permitted under Section 801 of the Junior Subordinated Indenture.

     6.5  NOTICES.  Any notice, request or other communication required or
permitted to be given hereunder to American General shall be given in writing by
delivering the same against receipt therefor by registered mail, hand delivery,
facsimile transmission (confirmed by registered mail) or telex, addressed to
American General, as follows (and if so given,

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<PAGE>
 
shall be deemed given when mailed; upon receipt of facsimile confirmation, if
sent by facsimile transmission; or upon receipt of an answer-back, if sent by
telex):

                    American General Corporation
                    2929 Allen Parkway
                    Houston, Texas  77019
                    Attention:  Treasury
                    Telecopy: (713) 522-3487

     Any notice, request or other communication required or permitted to be
given hereunder to the Holders shall be given by American General in the same
manner as notices are sent by American General Delaware to the Holders.

     6.6  GENDERS.  The masculine and neuter genders used herein shall include
the masculine, feminine and neuter genders.

     6.7  GUARANTEE NOT SEPARATELY TRANSFERABLE.  This Guarantee is solely for
the benefit of the Holders and is not separately transferable from the Preferred
Securities.

     6.8  GOVERNING LAW.  THIS GUARANTEE SHALL BE GOVERNED BY, AND CONSTRUED IN
ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

     6.9  SEVERABILITY.  In case any provision of this Guarantee shall be
invalid, illegal or unenforceable, the validity, legality and enforceability of
the remaining provisions shall not in any way be affected or impaired thereby.

     6.10 HEADINGS.  The Article and section headings herein are for convenience
only and shall not affect the construction hereof.

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<PAGE>
 
     IN WITNESS WHEREOF, American General has caused this Guarantee to be duly
executed as of the day and year first above written.

                                    AMERICAN GENERAL CORPORATION



                                    By:   /S/ AUSTIN P. YOUNG
                                    Name:     Austin P. Young
                                    Title:    Senior Vice President &
                                              Chief Financial Officer

ATTEST:


/S/ JOHN A. ADKINS
Secretary

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