<PAGE>   1
                                                                   EXHIBIT 10.34


           AMERICAN GENERAL CORPORATION RETIREMENT PLAN FOR DIRECTORS
           (AS AMENDED AND RESTATED EFFECTIVE AS OF JANUARY 29, 1998)

1. PURPOSE. This plan shall be known as the American General Corporation
Retirement Plan for Directors (the "Plan"). The Plan shall be maintained by
American General Corporation, a Texas corporation (the "Company") solely for the
purpose of providing retirement benefits to persons who have served as directors
of the Company and who, since July 1, 1965, have not been officers or employees
of the Company or of any subsidiary of which the Company owns directly or
indirectly more than 50% of the outstanding capital stock ("Directors").

2. PAYMENT OF BENEFITS. The benefits payable under the Plan will be paid from
the Company's general revenues as payments become due under the Plan, will not
be funded in advance through an arrangement constituting a qualified trust under
the Internal Revenue Code or through insurance annuity contracts, and will not
be subject to the jurisdiction of nor be guaranteed by the Pension Benefit
Guaranty Corporation. The Company shall not be required to establish any special
or separate fund or to make any other segregation of assets to assure the
payment of benefits under the Plan. Notwithstanding the foregoing provisions of
this Section 2, the Company may, in its discretion, establish a trust to pay
amounts becoming payable pursuant to this Plan, which trust shall be subject to
the claims of the Company's general creditors in the event of the Company's
bankruptcy or insolvency. Notwithstanding any establishment of such a trust, the
Company shall remain responsible for the payment of any amounts so payable which
are not so paid by such trust.

3. YEARS OF SERVICE. For all purposes of the Plan, a Director's Years of Service
shall be equal to the number of Years of Service credited under the terms of the
Plan as in effect on February 28, 1997. From and after March 1, 1997, no further
Years of Service shall be credited to Directors for purposes of benefits under
the Plan.

4. RETIREMENT BENEFITS. (a) A Director who retired or otherwise terminated
service as a Director prior to March 1, 1997 shall be entitled to benefits and
payments under the Plan based upon the terms and provisions of the Plan as in
effect on the date such Director retired or terminated service as a Director and
none of the provisions of this March 1, 1997 restatement of the Plan shall be
applicable to such Director.

(b) A Director who retires or otherwise terminates service as a Director on or
after March 1, 1997 shall receive a deferred account benefit determined pursuant
to Section 5 and Appendix A.

5. DEFERRED ACCOUNT. The March 1, 1997 accrued benefit under the Plan of each
Director who is serving as a Director on March 1, 1997 shall be converted to a
present dollar amount, based upon actuarial assumptions satisfactory to the
Administrator (hereinafter defined), and such dollar amount shall be converted
into a number of full and fractional "Units" equal in the aggregate to the value
of such present value dollar amount. For purposes of this Section 5, a
Director's March 1, 1997 Plan accrued benefit shall be equal to annual payments
payable commencing as of the date such Director attains the age of 70 for a
period of years equal to the Years of Service completed by the Director as of
February 28, 1997 but ending upon the Director's death if occurring prior to the
expiration of such period of years, with each such annual payment being equal to
the dollar amount of the annual retainer in effect for Directors on February 28,
1997. For all purposes of the Plan, a Unit shall be equal to the mean between
the high and low selling prices of the date as of which such value is being
determined of a share of Common Stock of the Company; provided, however, that
for purposes of effecting the conversion into Units of Directors' March 1, 1997
Plan accrued benefits as described under this Section 5, the value of a Unit
shall be equal to the average of the means between the high and low



                                       1
<PAGE>   2
selling prices during the period commencing April 28, 1997 and ending May 2,
1997, inclusive, of a share of Common Stock of the Company.

6. Benefit Not Assignable. A Director's rights under the Plan shall not be
subject to assignment, encumbrance, garnishment, attachment, or charge, whether
voluntary or involuntary.

7. Amendment and Termination of Plan. The Company reserves the right to amend or
terminate the Plan at any time by action of its Board of Directors, provided
that any such action shall not, without a Director's consent, adversely affect
any Director's right to a benefit which accrued pursuant to the provisions of
the Plan prior to such action.

8. Administration of Plan. The Plan shall be administered by an Administrator
who shall be a person or committee appointed by the Chairman of the Board. All
decisions that are made by the Administrator with respect to interpretation of
the terms of the Plan, with respect to the amount of benefits payable under the
Plan, and with respect to any questions or disputes arising under the Plan shall
be final and binding on the Company and the directors and their heirs or
beneficiaries.

9. Withholding. The Company shall have the right to deduct from any and all
amounts paid to any Director under this Plan any taxes required by law to be
withheld therefrom.

10. Construction. The Plan shall be governed by, and interpreted and enforced in
accordance with, the laws of the State of Texas and of the United States of
America.

    IN WITNESS WHEREOF, the Company has adopted this amended and restated Plan
as evidenced by the signatures affixed hereto of its duly authorized officers,
as of the 29th day of January, 1998.



                                                AMERICAN GENERAL CORPORATION


                                                By: /s/ MARK S. BERG
                                                    ----------------------------
                                                    Mark S. Berg
                                                    Senior Vice President and
                                                    General Counsel



                                       2
<PAGE>   3

                                                                      Appendix A


SECTION A1. DIRECTORS' ACCOUNT BALANCES. The Company shall maintain an
individual book account under the Plan for each Director having a deferred
account. Each Director shall initially have credited to his or her account the
number of Units calculated in respect of such Director pursuant to Section 5
hereof. Any dividends paid on Common Stock shall be credited to a Director's
account in respect of each Unit and deemed to be reinvested in additional Units.
In addition, the number of Units allocated to a Director's account shall be
adjusted to reflect stock dividends, splits and reclassifications, and similar
transactions affecting the value of Common Stock. At the time that the
Director's services as a Director cease, subject to Section 5 hereof, the
account balance will, until such time as it is paid to the Director in cash in
accordance with the Director's payment elections, be allocated among the
hypothetical investments permitted under A2(b)(ii) below, as may be elected by
the Director.

SECTION A2. PAYMENT ELECTIONS. (a) General Provisions. In connection with the
commencement of participation in this Plan, each Director shall make an election
(the "Payment Election") concerning the timing and form of distribution of the
amounts credited to his or her Plan account. Any payment from the Plan shall
commence following termination of the Director's services to the Company as a
Director, but in no event prior to one year after receipt by the Company of the
Director's initial Payment Election. The forms of benefit available under the
Plan shall be a lump sum payment or quarterly, semi-annual or annual
installments over a period not to exceed 15 years from the earliest date the
director may commence receiving payments hereunder.

    (b) Special Rule. (i) Subsequent Payment Elections may be made by a
Director, which shall supersede the initial Payment Election, but any such
subsequent Payment Election shall not be valid unless it is made prior to May of
the calendar year preceding the calendar year in which payments to the Director
hereunder are otherwise due to commence.

    (ii) If a Director has elected to receive installment payments of the amount
in his or her account, the Director may, at the Director's option, elect to
allocate the account, on or after the date on which he or she ceases to perform
services as a Director, among hypothetical investments in the AGC Stock Fund,
International Fund, Small-Cap Fund, Mid-Cap Fund, Equity Index Fund, Bond Fund
or Cash Fund under the American General Employees' Thrift and Incentive Plan and
shall be credited with a rate of return which said account would have earned had
it been invested in the fund elected. The Director may allocate and reallocate
his or her account among the funds in accordance with rules established by the
Administrator.

 SECTION A3. PAYMENTS TO A DECEASED DIRECTOR'S ESTATE. (a) In the event of a
Director's death before the balance of his or her account is fully paid, payment
of the balance of the Director's account shall then be made to his or her estate
in accordance with the manner selected by the Director prior to death, which
manner shall provide that (i) payment shall be made to the Director's estate in
the same manner as provided with respect to the payments to the Director or (ii)
the balance of the Director's account shall be determined as soon as practicable
following his or her death and this amount shall be paid in a single payment to
the Director's estate as soon as reasonably practicable thereafter. In the event
no election has been made, payment shall be made in accordance with clause (ii)
of the preceding sentence.

    (b)In the event of a Director's death before the balance of his or her
account is fully paid to the estate in installments, the Administrator may, upon
consideration of the application of the duly appointed administrator or executor
of the Director's estate, direct that the balance of the Director's account be
paid to the estate in a single payment. The payment shall be made at the time
specified by the Administrator.



                                       3
<PAGE>   4
SECTION A4. EFFECT OF A CHANGE IN CONTROL. (a) The provisions of the Plan and
this Appendix A to the contrary notwithstanding, upon the occurrence of a Change
in Control (as hereinafter defined) of the Company, any part of the account of a
Director who served as a Director on or after March 1, 1997 which is
hypothetically invested in American General Common Stock shall no longer be
deemed to be invested in Common Stock and shall immediately be deemed to be
invested at prime rate plus one percent (1%), as set at the beginning of each
calendar quarter and reported by the Company's lead lender."

     (b) For purposes of the Plan and this Appendix A, a Change in Control shall
be deemed to have occurred if the event set forth in any one of the following
paragraphs shall have occurred:

                    (a) any Person (as hereinafter defined) is or becomes the
               Beneficial Owner (as hereinafter defined), directly or
               indirectly, of securities of the Company (not including in the
               securities beneficially owned by such Person any securities
               acquired directly from the Company or its Affiliates (as
               hereinafter defined)) representing thirty percent (30%) or more
               of the combined voting power of the Company's then outstanding
               securities, excluding any Person who becomes such a Beneficial
               Owner in connection with a transaction described in clause (i) of
               paragraph (III) below; or

                    (b) the following individuals cease for any reason to
               constitute a majority of the number of directors then serving:
               individuals who, on February 1, 1998, constitute the Board and
               any new director (other than a director whose initial assumption
               of office is in connection with an actual or threatened election
               contest, including but not limited to a consent solicitation,
               relating to the election of directors of the Company) whose
               appointment or election by the Board or nomination for election
               by the Company's shareholders was approved or recommended by a
               vote of at least two-thirds (2/3) of the directors then still in
               office who either were directors on February 1, 1998 or whose
               appointment, election or nomination for election was previously
               so approved or recommended; or

                    (c) there is consummated a merger or consolidation of the
               Company or any direct or indirect subsidiary of the Company with
               any other corporation (or a share exchange between shareholders
               of the Company or any direct or indirect subsidiary of the
               Company and another corporation or entity pursuant to Article
               5.02 (or any successor provision thereto) of the Texas Business
               Corporation Act), other than (i) a merger or consolidation which
               would result in the voting securities of the Company outstanding
               immediately prior to such merger or consolidation continuing to
               represent (either by remaining outstanding or by being converted
               into voting securities of the surviving entity or any parent
               thereof), in combination with the ownership of any trustee or
               other fiduciary holding securities under an employee benefit plan
               of the Company or any subsidiary of the Company, at least
               fifty-one percent (51%) of the combined voting power of the
               securities of the Company or such surviving entity or any parent
               thereof outstanding immediately after such merger or
               consolidation, or (ii) a merger or consolidation effected to
               implement a recapitalization of the Company (or similar
               transaction) in which no Person is or becomes the Beneficial
               Owner, directly or indirectly, of securities of the Company
               representing thirty percent (30%) or more of the combined voting
               power of the Company's then outstanding securities; or


                                       4
<PAGE>   5

                         (IV) the shareholders of the Company approve a plan of
               complete liquidation or dissolution of the Company or there is
               consummated an agreement for the sale or disposition by the
               Company of all or substantially all of the Company's assets,
               other than a sale or disposition by the Company of all or
               substantially all of the Company's assets to an entity, at least
               fifty-one percent (51%) of the combined voting power of the
               voting securities of which are owned by shareholders of the
               Company in substantially the same proportions as their ownership
               of the Company immediately prior to such sale.

               Notwithstanding the foregoing, a "Change in Control" shall not be
               deemed to have occurred by virtue of the consummation of any
               transaction or series of integrated transactions immediately
               following which the record holders of the common stock of the
               Company immediately prior to such transaction or series of
               transactions continue to have substantially the same
               proportionate ownership in an entity which owns all or
               substantially all of the assets of the Company immediately
               following such transaction or series of transactions.

                    "Affiliate" shall have the meaning set forth in Rule 12b-2
               promulgated under Section 12 of the Exchange Act (as hereinafter
               defined).

                    "Beneficial Owner" shall have the meaning set forth in Rule
               13d_3 under the Exchange Act.

                    "Exchange Act" shall mean the Securities Exchange Act of
               1934, as amended from time to time.

                    "Person" shall have the meaning given in Section 3(a)(9) of
               the Exchange Act, as modified and used in Sections 13(d) and
               14(d) thereof, except that such term shall not include (i) the
               Company or any of its subsidiaries, (ii) a trustee or other
               fiduciary holding securities under an employee benefit plan of
               the Company or any of its Affiliates, (iii) an underwriter
               temporarily holding securities pursuant to an offering of such
               securities, or (iv) a corporation owned, directly or indirectly,
               by the shareholders of the Company in substantially the same
               proportions as their ownership of stock of the Company.




                                       5