<Page>

                                EXHIBIT (10)(p)

             FIRST AMENDMENT TO THE AGREEMENT AND PLAN OF MERGER

    This First Amendment to the Agreement and Plan of Merger ("First
Amendment") is entered into as of November 27, 2001, among International
Bancshares Corporation, a Texas corporation ("Parent"), NBC Acquisitions
Corp., a Delaware corporation and a direct wholly-owned subsidiary of Parent
("Delaware Sub"), and National Bancshares Corporation of Texas, a Texas
corporation (the "Company").

                              W I T N E S S E T H:

    WHEREAS, Parent, the Company and NBC Acquisition Corp, a Texas
corporation and predecessor in interest to Delaware Sub ("Texas Sub"),
entered into that certain Agreement and Plan of Merger dated as of July 30,
2001 (the "Merger Agreement"), providing for, among other things, (i) a
tender offer (the "Offer") by Texas Sub to purchase all of the outstanding
shares of common stock, par value $0.001 per share, of the Company (the
"Shares"), at a price per Share equal to the Merger Consideration (as defined
in the Merger Agreement), without interest, and (ii) subject to the
satisfaction of certain conditions set forth in the Merger Agreement, the
merger (the "Merger") of Texas Sub with and into the Company, with the
Company as the surviving corporation in the Merger;

    WHEREAS, on or about November 20, 2001, Texas Sub merged with and into
Delaware Sub, with Delaware Sub as the surviving corporation in such merger;

    WHEREAS, the parties desire to amend the Merger Agreement upon the terms
set forth herein; and

    WHEREAS, capitalized terms not otherwise defined herein shall have the
meaning ascribed thereto in the Merger Agreement;

    NOW, THEREFORE, in consideration of the premises and mutual covenants and
agreements of the Parties hereinafter contained, the Parties hereby agree as
follows:

    1.   EFFECTIVE TIME OF THE MERGER.  Section 1.4 of the Merger Agreement is
         hereby amended and restated to read in its entirety as follows:

    1.4  EFFECTIVE TIME OF THE MERGER.  The Merger shall become effective at
         the date and time (the "Effective Time") when Articles of Merger
         meeting the requirements of the Texas Business Corporation Act (the
         "TBCA") and a Certificate of Merger meeting the requirements of the
         Delaware General Corporation Law (the "DGCL") shall have been duly
         executed and filed in accordance with the TBCA and the DGCL,
         respectively, or at such other time as is specified in such Articles
         of Merger in accordance with the TBCA and such Certificate of Merger
         in accordance with the DGCL, which Articles of Merger and Certificate
         of Merger shall be filed as soon as practicable following fulfillment
         of the conditions set forth in Article VII hereof.

    2.   ARTICLES OF INCORPORATION.  Section 2.1 of the Merger Agreement is
         hereby amended and restated to read in its entirety as follows:

         2.1  ARTICLES OF INCORPORATION.  The Articles of Incorporation of the
    Company, as in effect immediately prior to the Effective Time, shall be the
    Articles of Incorporation of the Surviving Corporation, until further
    amended in accordance with their terms and as provided by law and this
    Agreement.

    3.   BY-LAWS.  Section 2.2 of the Merger Agreement is hereby amended and
         restated to read in its entirety as follows:

         2.2  BY-LAWS. The By-laws of the Company, as in effect immediately
    prior to the Effective Time, shall be the By-laws of the Surviving
    Corporation, and thereafter may be amended in accordance with their terms
    and as provided by law and this Agreement.

<Page>

    4.   EFFECTS OF MERGER.  Section 2.4 of the Merger Agreement is hereby
         amended and restated to read in its entirety as follows:

         2.4  EFFECTS OF MERGER. The Merger shall have the effects set forth
    in the TBCA and the DGCL.

    5.   COUNTERPARTS.  This First Amendment may be executed in one or more
         counterparts, all of which taken together shall constitute one
         instrument.

    6.   MISCELLANEOUS.  Except as otherwise expressly set forth in this
         First Amendment, the Merger Agreement shall remain in full force and
         effect, and the parties hereto shall be bound by the terms and
         conditions thereof, as herein amended.





                   [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]
<Page>

    IN WITNESS WHEREOF, the undersigned have duly executed this First
Amendment as of the date and year first above written.

                                       INTERNATIONAL BANCSHARES CORPORATION



                                       By: /s/ DENNIS E. NIXON
                                          -------------------------------------
                                          Dennis E. Nixon, President


                                       NBC ACQUISITIONS CORP.



                                       By: /s/ DENNIS E. NIXON
                                          -------------------------------------
                                          Dennis E. Nixon, President


                                       NATIONAL BANCSHARES CORPORATION OF TEXAS



                                       By: /s/ MARVIN E. MELSON
                                          -------------------------------------
                                          Marvin E. Melson, President