SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C. 20549


                                  FORM 8-K

                               CURRENT REPORT

  PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934


      Date of Report (Date of earliest event reported): April 1, 1998


                        AMBAC FINANCIAL GROUP, INC.

       Delaware                     1-10777                13-3621676
(State of incorporation)    (Commission File Number)     (I.R.S. Employer
                                                        Identification No.)

One State Street Plaza
New York, New York                                            10004
(Address of principal executive offices)                   (Zip Code)


                               (212) 668-0348
            (Registrant's telephone number, including area code)




ITEM 5.   OTHER EVENTS

      Ambac Financial Group, Inc. ("Ambac" or the "Registrant") is filing
herewith the following in connection with the offering of $200,000,000
principal amount of its 7.08% Debentures due March 31, 2098 (the
"Debentures") pursuant to the registration statement of the Registrant on
Form S-3 (No. 333-43695) filed with the Securities and Exchange Commission
under the Securities Act of 1933.


                             INDEX TO EXHIBITS

EXHIBIT
NUMBER                        EXHIBIT

5.1         Terms Agreement dated April 1, 1998 with respect to the
            Debentures.

5.2         Indenture, dated as of April, 1 1998, between Ambac and
            First Union National Bank.

5.3         Form of Debenture.



                                 SIGNATURE

      Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by
the undersigned hereunto duly authorized.

                                  AMBAC FINANCIAL GROUP, INC.


                                  By: _______________________


Date:  April 3, 1998



                             INDEX TO EXHIBITS

Exhibit
Number      Description of Exhibit
--------    ----------------------
5.1         Terms Agreement dated April 1, 1998 with respect to the
            Debentures.

5.2         Indenture, dated as of April, 1 1998, between Ambac and
            First Union National Bank.

5.3         Form of Debenture.
[{"type": "8-K", "sequence": "1", "secsgml_size_bytes": 2370}]
{"company-data": {"conformed-name": "AMBAC FINANCIAL GROUP INC", "cik": "0000874501", "assigned-sic": "6351", "irs-number": "133621676", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "8-K", "act": "34", "file-number": "001-10777", "film-number": "98590336"}, "business-address": {"street1": "ONE STATE ST PLZ", "city": "NEW YORK", "state": "NY", "zip": "10004", "phone": "2126680340"}, "mail-address": {"street1": "ONE STATE ST PLZ", "city": "NEW YORK", "state": "NY", "zip": "10004"}, "former-company": {"former-conformed-name": "AMBAC INC /DE/", "date-changed": "19930328"}}
SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C. 20549

                                  FORM 8-K

                               CURRENT REPORT

  PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934

      Date of Report (Date of earliest event reported): April 1, 1998

                        AMBAC FINANCIAL GROUP, INC.

       Delaware                     1-10777                13-3621676
(State of incorporation)    (Commission File Number)     (I.R.S. Employer
                                                        Identification No.)

One State Street Plaza
New York, New York                                            10004
(Address of principal executive offices)                   (Zip Code)

                               (212) 668-0348
            (Registrant's telephone number, including area code)

ITEM 5.   OTHER EVENTS

      Ambac Financial Group, Inc. ("Ambac" or the "Registrant") is filing
herewith the following in connection with the offering of $200,000,000
principal amount of its 7.08% Debentures due March 31, 2098 (the
"Debentures") pursuant to the registration statement of the Registrant on
Form S-3 (No. 333-43695) filed with the Securities and Exchange Commission
under the Securities Act of 1933.

                             INDEX TO EXHIBITS

EXHIBIT
NUMBER                        EXHIBIT

5.1         Terms Agreement dated April 1, 1998 with respect to the
            Debentures.

5.2         Indenture, dated as of April, 1 1998, between Ambac and
            First Union National Bank.

5.3         Form of Debenture.

                                 SIGNATURE

      Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by
the undersigned hereunto duly authorized.

                                  AMBAC FINANCIAL GROUP, INC.

                                  By: _______________________

Date:  April 3, 1998

                             INDEX TO EXHIBITS

Exhibit
Number      Description of Exhibit
--------    ----------------------
5.1         Terms Agreement dated April 1, 1998 with respect to the
            Debentures.

5.2         Indenture, dated as of April, 1 1998, between Ambac and
            First Union National Bank.

5.3         Form of Debenture.