Exhibit No. 5.1
                        AMBAC FINANCIAL GROUP, INC.
                          (a Delaware corporation)

                           Senior Debt Securities

                              TERMS AGREEMENT

                                                         April 1, 1998

To:   Ambac Financial Group, Inc.
      One State Street Plaza
      New York, New York 10004

Ladies and Gentlemen:

      We understand that Ambac Financial Group, Inc., a Delaware
corporation (the "Company"), proposes to issue and sell $200,000,000
aggregate principal amount of its Senior Debt Securities (such securities
being hereinafter referred to as the "Underwritten Securities"). Subject to
the terms and conditions set forth and incorporated by reference herein,
the underwriters named below (the "Underwriters") offer to purchase,
severally and not jointly, the principal amount of Underwritten Securities
set forth opposite their names below at the purchase price set forth below.

                                                Principal Amount of
        Underwriter                             Underwritten Securities

Merrill Lynch, Pierce, Fenner & Smith
   Incorporated.................................        $33,600,000
Goldman, Sachs & Co.............................         33,600,000
PaineWebber Incorporated........................         33,600,000
Prudential Securities Incorporated..............         33,600,000
Smith Barney Inc................................         33,600,000
BT Alex. Brown Incorporated.....................          2,000,000
Robert W. Baird & Co. Incorporated..............          2,000,000
Bear, Stearns & Co. Inc.........................          2,000,000
CIBC Oppenheimer Corp...........................          2,000,000
Cowen & Company.................................          2,000,000
Dain Rauscher Incorporated......................          2,000,000
Donaldson, Lufkin & Jenrette
  Securities Corporation........................          2,000,000
A.G. Edwards & Sons, Inc........................          2,000,000
EVEREN Securities, Inc..........................          2,000,000
Legg Mason Wood Walker, Incorporated............          2,000,000
Piper Jaffray Inc...............................          2,000,000
Raymond James & Associates, Inc.................          2,000,000
The Robinson-Humphrey Company, LLC..............          2,000,000
Tucker Anthony Incorporated.....................          2,000,000
US Clearing Corp................................          2,000,000
Wheat First Securities, Inc.....................          2,000,000
                                                       ------------
Total...........................................       $200,000,000
                                                       ============



      The Underwritten Securities shall have the following terms:

Title:                        7.08% Debentures Due March 31, 2098.
Rank:                         Senior Debt.
Ratings:                      Moody's Investor's Service, Inc. - Aa2 and
                              Standard & Poor's Ratings Group - AA.
Aggregate principal amount:   $200,000,000.
Denominations:                $25.00 and integral multiples thereof.
Currency of payment:          United States Dollars.
Interest rate or formula:     7.08% per annum.
Interest payment dates:       Each March 31, June 30, September 30 and
                              December 31.
Regular                       record dates: Each March 15, June 15,
                              September 15 and December 15.
Stated maturity date:         March 31, 2098.
Redemption provisions:        Except as set forth below, the Debentures are
                              not redeemable prior to March 31, 2003. On or
                              after March 31, 2003, the Company, at its
                              option, may redeem the Debentures, in whole
                              at any time or in part from time to time, on
                              not less than 30 days but not more than 60
                              days notice, at a redemption price equal to
                              100% of the principal amount, plus accrued
                              interest to the date of redemption. In
                              addition, under certain circumstances
                              involving a Tax Event, the Company will have
                              the right, within 90 days following the
                              occurrence of such Tax Event, to redeem the
                              Debentures in whole (but not in part) at 100%
                              of their principal amount, plus accrued
                              interest to the date of redemption, as more
                              fully described in the Prospectus Supplement.

Right to Shorten Maturity:    Upon the occurrence of a Tax Event (as
                              defined in the Prospectus Supplement), the
                              Company will have the right to shorten the
                              maturity of the Debentures to the minimum
                              extent required such that, after shortening
                              the maturity, the Company will be able to
                              deduct interest paid on the Debentures for
                              United States federal income tax purposes, as
                              more fully described in the Prospectus
                              Supplement.
Sinking fund requirements:    None.
Conversion provisions:        None.
Listing requirements:         The Company will make application to list the
                              Debentures for trading on the New York Stock
                              Exchange.
Black-out provisions:         Between the date hereof and April 15, 1998,
                              the Company will not, without the prior
                              written consent of the Representatives,
                              directly or indirectly, issue, sell, offer or
                              contract to sell, grant any option for the
                              sale of, or otherwise dispose of, any debt
                              securities of the Company.
Fixed or Variable Price
Offering:                     Fixed Price Offering Initial public offering
                              price: 100% of the principal amount, plus
                              accrued interest, if any, from April 6, 1998.
Purchase price:               96.85% of the principal amount.
Form:                         Global certificates representing the
                              Underwritten Securities registered in the
                              name of Cede & Co., as nominee for The
                              Depository Trust Company.

Other terms and conditions:   The Underwritten Securities will be issued
                              under an indenture, dated as of April 1, 1998
                              between the Company and First Union National
                              Bank, as Trustee (the "1998 Indenture"). All
                              references to the "Indenture" in the
                              Underwriting Agreement shall be deemed to
                              refer to the 1998 Indenture.
Closing                       date and location: April 6, 1998; Brown &
                              Wood LLP, One World Trade Center, New York,
                              New York 10048.
Co-Managers/Representatives:  Merrill Lynch, Pierce, Fenner & Smith
                              Incorporated, Goldman, Sachs & Co.,
                              PaineWebber Incorporated, Prudential
                              Securities Incorporated and Smith Barney Inc.
Notices:                      Notices to the Underwriters shall be directed
                              to the Representatives, c/o Merrill Lynch,
                              Pierce, Fenner & Smith Incorporated, World
                              Financial Center, North Tower, New York, New
                              York 10281-1201, Attention: Tony Ursano.

      All of the provisions contained in the Company's Underwriting
Agreement, dated April 1, 1998 (the "Underwriting Agreement"), are hereby
incorporated by reference in their entirety herein and shall be deemed to
be a part of this Terms Agreement to the same extent as if such provisions
had been set forth in full herein. Unless otherwise specified herein, terms
defined in the Underwriting Agreement are used herein as therein defined.

      This Agreement shall be governed by the laws of the State of New York
applicable to agreements made and to be performed wholly within such State.

      If the foregoing is in accordance with your understanding of the
agreement among the Underwriters and the Company, please sign and return to
the undersigned a counterpart hereof, whereupon this instrument, along with
all counterparts and together with the Underwriting Agreement, shall be a
binding agreement among the Underwriters named herein and the Company in
accordance with its terms and the terms of the Underwriting Agreement.

                               Very truly yours,

                               MERRILL LYNCH, PIERCE, FENNER & SMITH
                                  INCORPORATED

                               GOLDMAN, SACHS & CO.

                               PAINEWEBBER INCORPORATED

                               PRUDENTIAL SECURITIES INCORPORATED

                               SMITH BARNEY INC.

                               By:  Merrill Lynch, Pierce, Fenner & Smith
                                       Incorporated

                               By _______________________________________
                                            Authorized Signatory

                               Acting on behalf of itself and as
                               Representative of the other named
                               Underwriters.


Accepted:

AMBAC FINANCIAL GROUP, INC.

By _________________________________
Name:  Richard B. Gross
Title: Senior Vice President,
       General Counsel and Secretary