<PAGE>
 
                                                                    Exhibit 8(a)

                                VINSON & ELKINS
                               ATTORNEYS AT LAW

                            VINSON & ELKINS L.L.P.
                             2300 FIRST CITY TOWER
                              1001 FANNIN STREET

                           HOUSTON, TEXAS 77002-6760

                           TELEPHONE (713) 758-2222
                              FAX (713) 758-2346



     (713)  758-2192                                       (713) 615-5210

                                January 31, 1996



American General Corporation
2929 Allen Parkway
Houston, Texas  77019

Ladies and Gentlemen:

     We have been acting as counsel to American General Corporation
("Purchaser") and its wholly-owned subsidiary, AGC Life Insurance Company
("Sub") in connection with the transactions contemplated by the Agreement and
Plan of Merger, dated as of October 19, 1995 and amended as of January 25, 1996,
by and among Purchaser, Sub and Independent Insurance Group, Inc. (the
"Company") (the "Merger Agreement").  The delivery of an opinion at the
Effective Time,/1/ in substance to the effect hereinafter stated, is a condition
to the obligations of Purchaser and Sub to consummate the Merger pursuant to
Section 8.3(b) of the Merger Agreement.

     Our opinion is based upon (i) the Merger Agreement, (ii) the facts and
documents set forth or referenced in the Proxy Statement/Prospectus filed with
the Securities and Exchange Commission as part of the Registration Statement
with respect to the Merger (the "Registration  Statement"), and (iii) the
representations referenced below as to the existence of certain facts.  Our
opinion is expressly conditioned upon the initial and continuing accuracy of all
of such facts, documents and representations.

     In rendering this opinion, we have assumed that the Merger will be
consummated at the Effective Time strictly in accordance with the terms of the
Merger Agreement and that there are no other agreements, arrangements, or
understandings among any of Purchaser, Sub, the Company or the stockholders of
the Company other than those described or referenced in the Merger Agreement or
the Registration Statement.  In addition, our opinion is expressly conditioned
upon our receipt, at or prior to the Effective Time, of certificates executed by
officers of Purchaser, Sub and the Company, in form and substance satisfactory
to us and on which we may rely, as to certain facts relating to, and knowledge
and intentions of, Purchaser, Sub and the Company with respect to the Merger.


----------------
/1/   Capitalized terms used but not defined herein have the meanings ascribed
      to them in the Merger Agreement.
<PAGE>
 
American General Corporation
Page 2
January 31, 1996


     In rendering our opinion, we have considered the applicable provisions of
the Internal Revenue Code of 1986, as amended (the "Code"), Treasury regulations
promulgated thereunder, other relevant statutes, pertinent judicial authorities,
interpretive rulings of the Internal Revenue Service and such other authorities
as we have considered relevant.  It should be noted that statutes, regulations,
judicial decisions and administrative interpretations are subject to change at
any time, in some circumstances with retroactive effect.  A material change in
the authorities upon which our opinion is based could affect our conclusions.

     Based solely upon the foregoing, it is our opinion that, under current law:

          The Merger would be treated for Federal income tax purposes as a
     reorganization within the meaning of Section 368(a) of the Code, and that
     Purchaser, Sub and the Company would each be a party to that reorganization
     within the meaning of Section 368(b) of the Code.  In addition, the
     material federal income tax consequences of the Merger to the shareholders
     of Independent would be as set forth in the Registration Statement.

     Except as set forth above, we express no opinion as to the tax treatment of
the Merger or to the tax treatment of any conditions existing at the time of, or
effects resulting from, the transactions which are not specifically addressed in
the foregoing opinion.

     This opinion is given to you by us solely for your use and is not to be
quoted or otherwise referred to or furnished to any governmental agency (other
than to the Securities and Exchange Commission as an exhibit to the Registration
Statement or to the Internal Revenue Service in connection with an examination
of the transactions contemplated by the Merger Agreement) or to other persons
without our prior written consent.

     We hereby consent to the use of our name in the Registration Statement and
to the filing of this letter as an exhibit to the Registration Statement. In
giving this consent, however, we do not hereby admit that we are within the
category of persons whose consent is required under Section 7 of the Securities
Act of 1933, as amended, or the rules and regulations of the Securities and
Exchange Commission thereunder.

                                    Very truly yours,
                                    
                                    /s/VINSON & ELKINS L.L.P.

                                    VINSON & ELKINS L.L.P.