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                                    EXHIBIT 4


WHEREAS, on February 18, 1997, AFC Holding Company (formerly American Financial
Group, Inc.) filed a Registration Statement Number 333-21995 on Form S-3 (the
"Registration Statement") with the Securities and Exchange Commission ("SEC")
for the purpose, among others, of registering unsecured debt securities to be
issued by AFC Holding Company ("Debt Securities"); and

WHEREAS, on December 2, 1997, the shareholders of AFC Holding Company approved a
reorganization pursuant to which AFC Holding Company became a wholly-owned
subsidiary of the Corporation; and

WHEREAS, on or about December 3, 1997, the Corporation, AFC Holding Company and
Star Bank, N.A., as parties to an Indenture dated November 12, 1997 with respect
to the Debt Securities, executed and delivered a Supplemental Indenture pursuant
to which the Corporation has been substituted as obligor for all purposes under
the Debt Securities; and

WHEREAS, this Board of Directors has, after due deliberation, determined that it
is in the best interests of the Corporation and all its shareholders that the
Corporation issue a series of Debt Securities to be known as the "7-1/8% Senior
Debentures Due 2007" (the "Senior Debentures"); and

NOW, THEREFORE, BE IT

RESOLVED, that the Corporation be, and it hereby is, authorized to issue and to
sell up to One Hundred Million Dollars ($100,000,000) in aggregate principal
amount of 7-1/8% Senior Debentures Due December 15, 2007, which Senior
Debentures shall bear interest from the date of the issuance thereof at the rate
of 7-1/8% per annum and with interest payable semiannually on June 15 and
December 15 of each year, commencing June 15, 1998; and, BE IT

RESOLVED FURTHER, that the Senior Debentures will initially be issued in the
form of one global note (the "Global Note") held in book entry form and
deposited on the date of the closing of the sale of the Senior Debentures with,
on or behalf of, The Depository Trust Company ("DTC") and registered in the name
of Cede & Co., as nominee of DTC (such nominee being referred to as the "Global
Debenture Holder"); and, BE IT

RESOLVED FURTHER, that so long as the Global Note holder is the registered owner
of the Global Note, the Global Note holder will be considered the sole holder
under the Indenture of the Senior Debentures; and, BE IT

RESOLVED FURTHER, that One East Fourth Street, Cincinnati, Ohio 45202 shall be
the place where: (i) the principal, interest and premium (if any) are payable on
the Senior Debentures; (ii) Senior Debentures may be surrendered for
registration or transfer; (iii) 



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Senior Debentures may be surrendered for exchange; and (iv) notices and demands
to or upon the Corporation in respect of Senior Debentures may be served; and,
BE IT

RESOLVED FURTHER, that the Senior Debentures shall be redeemable, in whole or in
part, at the option of the Corporation at any time, on not less than 30 nor more
than 60 days' notice, at a redemption price equal to the sum of (i) the
principal amount of Senior Debentures being redeemed plus interest thereon to
the redemption date; and (ii) the Make-Whole Amount (as defined in the
Prospectus Supplement dated December 10, 1997), if any, but shall not be subject
to any sinking fund; and, BE IT

RESOLVED FURTHER, that the Senior Debentures shall have such other terms and
conditions, consistent with the foregoing, as are set forth in the Terms
Agreement (attached hereto) and the Prospectus Supplement dated December 10,
1997, as the same may be amended, modified or supplemented from time to time by
or under the direction of the officers of the Corporation (as so amended,
modified or supplemented, the "Prospectus Supplement"); and, BE IT

RESOLVED FURTHER, that any one (1) or more of the officers of the Corporation
be, and they hereby are, authorized and directed, on behalf of the Corporation,
to execute and to deliver any and all documents, including (without limitation)
an Indenture with respect to the Senior Debentures, certificates evidencing the
Senior Debentures, agreements with underwriters or others for the marketing and
sale of the Senior Debentures and other certificates, ancillary agreements or
other documents that such officer or officers may deem necessary or appropriate
in connection with the issuance and sale of the Senior Debentures or to give
full force and effect to the purposes of the foregoing resolutions; and, BE IT

RESOLVED FURTHER, that any one (1) or more of the officers of the Corporation
be, and they hereby are, authorized to take (or to cause to be taken), on behalf
of the Corporation, any and all actions, including (without limitation)
completing and filing with the SEC the Prospectus Supplement, that such officer
or officers may deem necessary or appropriate in connection with the issuance
and sale of the Senior Debentures or to give full force and effect to the
purposes of the foregoing resolutions.





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                         AMERICAN FINANCIAL GROUP, INC.
                                   ("COMPANY")


                                 DEBT SECURITIES


                                 TERMS AGREEMENT
                                 ---------------




                                                               December 10, 1997


TO:  The Representative of the Underwriters identified herein



Dear Sirs:

         The undersigned agrees to sell to the several Underwriters named in
Schedule A hereto for their respective accounts on and subject to the terms and
conditions of the Underwriting Agreement filed as an exhibit to the Company's
registration statement on Form S-3 (No. 333-21995) ("Underwriting Agreement"),
the following securities ("Offered Securities") on the following terms:

         TITLE:  7.125% Senior Debentures Due 2007.

         PRINCIPAL AMOUNT:  $100,000,000

         INTEREST: 7.125% per annum, from December 15, 1997, payable
         semiannually on June 15 and December 15, commencing June 15, 1998, to
         holders of record on the preceding June 1 or December 1, as the case
         may be.

         MATURITY:  December 15, 2007

         OPTIONAL REDEMPTION:  As set forth on Schedule B attached hereto.

         SINKING FUND:  None



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         LISTING:  None

         RATING: The Company has been informed that the Offered Securities have
         been assigned the following ratings: S&P, "BBB"; Moody's, "Baa3."

         DELAYED DELIVERY CONTRACTS:  Not Applicable.

         PURCHASE PRICE:  99.166% of principal amount.

         EXPECTED REOFFERING PRICE: 99.816% of principal amount, subject to
         change by the Representative.

         CLOSING: 9:00 A.M. on December 15, 1997, at Taft, Stettinius &
         Hollister, Cincinnati, Ohio, in Federal (same day) funds.

         SETTLEMENT AND TRADING: Book-Entry Only via DTC. Securities will trade
         in DTC's Same Day Funds Settlement System.

         BLACKOUT:  Through the Closing Date.


         The respective principal amounts of the Offered Securities to be
purchased by each of the Underwriters are set forth opposite their names in
Schedule A hereto.

         The provisions of the Underwriting Agreement are incorporated herein by
reference.

         The Offered Securities will be made available for checking and
packaging at the office of the Representative at least 24 hours prior to the
Closing Date.

         For purposes of Section 6 of the Underwriting Agreement, the only
information furnished to the Company by any Underwriter for use in the
Prospectus consists of the following information in the Prospectus furnished on
behalf of each Underwriter: the last paragraph at the bottom of the prospectus
supplement cover page concerning the terms of the offering by the Underwriters,
the legend stabilizing on the inside front cover page of the prospectus
supplement and, the concession and reallowance figures appearing under the
caption "Underwriting" in the prospectus supplement and the information
contained in the paragraphs under the caption "Underwriting" in the prospectus
supplement.

         If the foregoing is in accordance with your understanding of our
agreement, kindly sign and return to the Company one of the counterparts hereof,
whereupon it will


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become a binding agreement between the Company and the several Underwriters in
accordance with its terms.

                                          Very truly yours,

                                          AMERICAN FINANCIAL GROUP, INC.



                                          By:
                                             -----------------------------------
                                                James E. Evans
                                                Senior Vice President


The foregoing Terms Agreement is hereby confirmed and accepted as of the date
first above written.

CREDIT SUISSE FIRST BOSTON CORPORATION



By:
   -----------------------------------------
               [Insert title]

[Acting on behalf of itself and as the
Representative of the several Underwriters.]



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                                   SCHEDULE A





          UNDERWRITER                               PRINCIPAL AMOUNT
          -----------                               ----------------

                                                           
Credit Suisse First Boston Corporation               $ 33,400,000

Bear, Stearns & Co. Inc.                             $ 33,300,000

Donaldson, Lufkin & Securities Corp.                 $ 33,300,000


                Total................................$100,000,000
                                                     ============




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                                   SCHEDULE B

Optional Redemption
- -------------------

         The Senior Debentures will be subject to redemption at the option of
the Company, in whole or in part, upon not less than 30 nor more than 60 days'
notice, at a redemption price equal to the sum of (i) the principal amount of
the Senior Debentures being redeemed plus accrued interest thereon to the
redemption date, and (ii) the Make-Whole Amount (as defined below), if any, with
respect to such Senior Debentures.

         "Make-Whole Amount" means, in connection with any optional redemption
of any Senior Debentures, the excess, if any, of (i) the sum, as determined by a
Quotation Agent (as defined herein) of the present values of the principal
amount of such Senior Debentures, together with scheduled payments of interest
from the redemption date to the Stated Maturity of the Senior Debentures, in
each case discounted to the redemption date on a semi-annual basis (assuming a
360-day year consisting of twelve 30-day months) at the Adjusted Treasury Rate
(as defined herein) over (ii) 100% of the principal amount of the Senior
Debentures to be redeemed.

         "Adjusted Treasury Rate" means, with respect to any redemption date,
the rate per annum equal to the semi-annual equivalent yield to maturity of the
Comparable Treasury Issue, calculated using a price for the Comparable Treasury
Issue (expressed as a percentage of its principal amount) equal to the
Comparable Treasury Price for such redemption date, calculated on the third
Business Day preceding the redemption date, plus in each case .20%. (20 basis
points).

         "Comparable Treasury Issue" means the U. S. Treasury 6.125% Note due
August 15, 2007. If such security shall cease to be outstanding then Comparable
Treasury Issue shall mean the United States Treasury security selected by the
Quotation Agent as having a maturity comparable to the remaining term from the
redemption date to the Stated Maturity Date of the Senior Debentures that would
be utilized, at the time of selection and in accordance with customary financial
practice, in pricing new issues of corporate debt securities of comparable
maturity to the remaining term of the Senior Debentures.

         "Quotation Agent" means the Reference Treasury Dealer selected by the
Indenture Trustee after consultation with the Company. "Reference Treasury
Dealer" means a primary U.S. Government securities dealer.

         "Comparable Treasury Price" means, with respect to any redemption date,
(i) the average of the bid and asked prices for the Comparable Treasury Issue
(expressed in each case as a percentage of its principal amount) on the third
Business Day preceding such redemption date, as set forth in the daily
statistical release (or any successor release) published by the Federal Reserve
Bank of New York and designated "Composite 3:30 p.m. Quotations for U.S.
Government Securities" or (ii) if such release (or any successor release) is not
published or does not contain such prices on such Business Day, (A) the 


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average of the Reference Treasury Dealer Quotations for such redemption date,
after excluding the highest and lowest such Reference Treasury Dealer
Quotations, or (B) if the Indenture Trustee obtains fewer than three such
Reference Treasury Dealer Quotations, the average of such Quotations.

         "Reference Treasury Dealer Quotations" means, with respect to each
Reference Treasury Dealer and any prepayment date, the average, as determined by
the Indenture Trustee, of the bid and asked prices for the Comparable Treasury
Issue (expressed in each case as a percentage of its principal amount) quoted in
writing to the Indenture Trustee by such Reference Treasury Dealer at 5:00 p.m.,
New York City time, on the third Business Day preceding such redemption date.



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