<PAGE>   1
 
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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
                                  FORM 10-K/A
                               (AMENDMENT NO. 1)
[ X ]  ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(D) OF
       THE SECURITIES EXCHANGE ACT OF 1934
 
       For the fiscal year ended December 31, 1998
 
                                       OR
 
[   ]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF
       THE SECURITIES EXCHANGE ACT of 1934
 
       For the transition period from
     ----------------------------- to
     -----------------------------
                        COMMISSION FILE NUMBER 000-21629
 
                            THE KROLL-O'GARA COMPANY
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                                      <C>
                          OHIO                                                  31-1470817
              (State or other jurisdiction                                   (I.R.S. Employer
                   of incorporation)                                       Identification No.)
</TABLE>
 
                               9113 LESAINT DRIVE
                             FAIRFIELD, OHIO 45014
                                 (513) 874-2112
  (Address, including zip code, and telephone number, including area code, of
                   registrant's principal executive offices)
 
Securities Registered Pursuant to Section 12(b) of the Act:     None
Securities Registered Pursuant to Section 12(g) of the Act:     Common Stock,
$.01 par value
 
Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.  Yes [ X ]      No [   ]
 
Indicate by check mark if disclosure of delinquent filers pursuant to Item 405
of Regulation S-K is not contained herein, and will not be contained, to the
best of registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment of this
Form 10-K  [ ]
 
The aggregate market value of the Common Stock of the registrant held by
non-affiliates of the registrant was approximately $373,623,141 as of March 31,
1999. As of March 31, 1999, 20,870,079 shares of Common Stock were outstanding.
 
                  DOCUMENTS INCORPORATED BY REFERENCE -- NONE
 
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<PAGE>   2

Explanatory Note: This amended report is being filed to furnish the Part III
information set forth below.
 
                                    PART III
 
ITEM 10.  DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT
 
     The following table sets forth certain information as of March 31, 1999
concerning each of Kroll-O'Gara's executive officers and directors:
 
<TABLE>
<CAPTION>
                   NAME                     AGE                     POSITION
                   ----                     ---                     --------
<S>                                         <C>    <C>
Jules B. Kroll............................  57     Chairman of the Board, Chief Executive
                                                   Officer and Director
Thomas M. O'Gara..........................  48     Vice Chairman of the Board and Director
Wilfred T. O'Gara.........................  41     President, Chief Operating Officer and
                                                   Director
Nicholas P. Carpinello....................  49     Controller and Treasurer
Michael G. Cherkasky......................  49     Chief Operating Officer -- Investigations
                                                   and Intelligence Group and Director
Marshall S. Cogan.........................  61     Director
Abram S. Gordon...........................  35     Vice President, General Counsel and
                                                   Secretary
Michael J. Lennon.........................  42     Chief Operating Officer -- Security
                                                   Products and Services and Director
Raymond E. Mabus..........................  50     Director
Nazzareno E. Paciotti.....................  53     Chief Financial Officer
Hugh E. Price.............................  62     Director
Jerry E. Ritter...........................  64     Director
William S. Sessions.......................  68     Director
Howard I. Smith...........................  54     Director
</TABLE>
 
     JULES B. KROLL has been Chairman of the Board and Chief Executive Officer
of Kroll-O'Gara since the Kroll Holdings merger on December 1, 1997. He founded
Kroll-O'Gara's Kroll Associates, Inc. subsidiary in 1972 and has been the
Chairman of the Board and Chief Executive Officer of Kroll Associates and Kroll
Holdings since their foundings. Mr. Kroll also is a director of United Auto
Group, Inc. He has been a director of Kroll-O'Gara since December 1997.
 
     THOMAS M. O'GARA has been Vice Chairman of the Board of Kroll-O'Gara since
the Kroll Holdings merger. He served as Chairman of the Board of Kroll-O'Gara
from August 1996 until December 1997. Mr. O'Gara has also been Chairman of the
Board of OHE since 1990 and was OHE's Chief Executive Officer from 1990 until
1995. He has been a director of Kroll-O'Gara since August 1996 and a director of
OHE since 1988. Mr. O'Gara has held numerous executive officer and director
positions with Kroll-O'Gara, its subsidiaries and its predecessors since 1975.
From 1984 until 1986, Mr. O'Gara also was Honorary Consul General for the
Sultanate of Oman. Thomas M. O'Gara and Wilfred T. O'Gara are brothers.
 
     WILFRED T. O'GARA has been President and Chief Operating Officer of
Kroll-O'Gara since the Kroll Holdings merger prior to which he had served as
Kroll-O'Gara's Chief Executive Officer since August 1996. Mr. O'Gara has been
associated with Kroll-O'Gara, its subsidiaries and its predecessors since 1983
and has held numerous executive officer and director positions, including
serving as Chief Executive Officer of OHE since January 1996, President and
Chief Operating Officer of OHE from 1991 through 1995 and Vice
President -- Sales and Marketing of OHE from 1988 until 1991. Mr. O'Gara has
been a director of Kroll-O'Gara since August 1996 and a director of OHE since
1991. Mr. O'Gara also is a director of LSI Industries, Inc.
 
                                     -2-
<PAGE>   3
 
     NICHOLAS P. CARPINELLO has been Controller and Treasurer of Kroll-O'Gara
since the Kroll Holdings merger. From August 1996 until December 1997 he served
as Kroll-O'Gara's Executive Vice President, Chief Financial Officer and
Treasurer, positions he also has held with OHE since 1993. Mr. Carpinello has
been associated with Kroll-O'Gara and its predecessors since 1984. From 1975
until 1984, he was employed by Arthur Andersen LLP where he served as a manager
in the audit and small business consulting divisions.
 
     MICHAEL G. CHERKASKY became Chief Operating Officer of Kroll-O'Gara's
Investigations and Intelligence Group in December 1997. Prior to the Kroll
Holdings merger he had been an Executive Managing Director of Kroll Holdings
since April 1997 and Chief Operating Officer of Kroll Holdings since January
1997. From November 1995 to January 1997, he was the head of Kroll Holdings'
North American Region and from February 1994 to November 1995 he was the head of
Kroll Holdings' Monitoring Group. From June 1993 to November 1993, Mr. Cherkasky
was a candidate for public office. From 1978 to June 1993, Mr. Cherkasky was
with the District Attorney's office for New York County, his last position being
Chief of the Investigation Division. He became a director of Kroll-O'Gara in
December 1997.
 
     MARSHALL S. COGAN has been Vice Chairman of Foamex International, Inc., a
manufacturer of polyurethane foam products, since May 1997 and Chairman and
Chief Executive Officer of United Auto Group, a franchisor of car and light
truck dealerships, since April 1997. Mr. Cogan was Chairman of the Board and
Chairman of the Executive Committee of Foamex International from 1993 until 1997
and was Chief Executive Officer of Foamex International from 1994 until 1997.
Since 1974, Mr. Cogan has been the principal shareholder, Chairman or Co-
Chairman of the Board of Directors, and Chief Executive Officer or Co-Chief
Executive Officer, of Trace International Holdings, Inc., a holding company
operating businesses in the auto sales, foam, textile and publishing industries.
Mr. Cogan has been a director of Kroll-O'Gara since December 1997.
 
     ABRAM S. GORDON is Vice President, General Counsel and Secretary of
Kroll-O'Gara. Prior to joining Kroll-O'Gara in January 1997, he was with the law
firm of Taft, Stettinius & Hollister LLP, Cincinnati, Ohio, from October 1987
until December 1996.
 
     MICHAEL J. LENNON became Chief Operating Officer of Kroll-O'Gara's Security
Products and Services Group in December 1997. He also has been the President and
Chief Operating Officer of OHE since January 1996. Mr. Lennon joined OHE in
February 1994 as Manager of Commercial and Military Programs; he became Vice
President for Sales, Marketing and Program Management in October 1994 and served
OHE in that capacity through 1995. Prior to joining OHE, Mr. Lennon had 15
years' experience in engineering, manufacturing, quality control and marketing
with General Electric Company, which he joined in 1979. From 1990 to 1994, he
was Manager of Advanced Technology Marketing for their G.E. Aircraft Engines
business. He became a director of Kroll-O'Gara in March 1998.
 
     RAYMOND E. MABUS is President of International Management and Development
Group Ltd., a provider of workforce analysis, foreign investment planning and
resource generation services, and of counsel to the law firm of Baker,
Donaldson, Bearman and Caldwell. He also manages a family timber business. He
served as the United States Ambassador to the Kingdom of Saudi Arabia from 1994
until 1996, as a consultant to Mobil Telecommunications Technology from 1992
until 1994 and as Governor of the State of Mississippi from 1988 until 1992. Mr.
Mabus has been a director of Kroll-O'Gara since November 1996.
 
     NAZZARENO E. PACIOTTI has been Chief Financial Officer of Kroll-O'Gara
since the Kroll Holdings merger. Prior to the Kroll Holdings merger he had been
the Chief Financial Officer of Kroll Holdings since 1992. From 1990 to 1992, he
was a Managing Director and the Controller of the Henley Group (the parent of
PneumoAbex Inc. and Fisher Scientific, a laboratory supply company) and from
1988 to 1990, he was a Vice President and the Controller of PneumoAbex Inc., an
aerospace contractor specializing in the manufacture of landing gear and flight
actuating systems.
 
     HUGH E. PRICE is engaged in business development activities for
Kroll-O'Gara. During 1995 and 1996, prior to joining Kroll-O'Gara, he was a
consultant to various businesses and organizations. Until his retirement in
1995, Mr. Price had been employed by the Central Intelligence Agency since 1964.
His positions with the Agency included Deputy and Associate Deputy Director for
Operations (1991-1995), Chief
 
                                     -3-
<PAGE>   4
 
and Deputy Chief for Counterintelligence (1988-1990) and Director of Personnel
(1986-1988). Mr. Price became a director of Kroll-O'Gara in October 1996.
 
     JERRY E. RITTER is currently a consultant to Anheuser-Busch Companies,
Inc., a company engaged in the brewing and family entertainment businesses. He
also is Chairman of the Board of Clark Enterprises, Inc., the general partner of
the Kiel Center and the St. Louis Blues Hockey Club. From 1990 until 1996, Mr.
Ritter served as Executive Vice President and Chief Financial and Administrative
Officer for Anheuser-Busch Companies, Inc. Prior to that time, he served
Anheuser-Busch in various other managerial and executive capacities. Mr. Ritter
also is a director of The Earthgrains Company, Brown Group, Inc. and OmniQuip
International, Inc. He became a director of Kroll-O'Gara in January 1997.
 
     WILLIAM S. SESSIONS is a partner in the law firm of Sessions & Sessions
L.C. and is a consultant to various public and private businesses. From 1987
until 1993, Mr. Sessions was Director of the Federal Bureau of Investigation. He
served as a United States District Judge for the Western District of Texas from
1974 until 1987. Mr. Sessions is a director of Zenith National Insurance
Company. He has been a director of Kroll-O'Gara since November 1996.
 
     HOWARD I. SMITH has been Executive Vice President, Chief Financial Officer
and Comptroller of AIG since 1996. From 1984 until 1996, Mr. Smith was Senior
Vice President and Comptroller of AIG. From 1975 until 1984 Mr. Smith was a
partner in the independent public accounting firm of Coopers & Lybrand. Mr.
Smith also is a director of AIG, 20th Century Industries, International Lease
Finance Corporation and Transatlantic Holdings, Inc. He became a director of
Kroll-O'Gara in December 1997.
 
     Directors of Kroll-O'Gara are elected annually. Officers of Kroll-O'Gara
are elected annually and serve at the discretion of the Board of Directors.
 
     SECTION 16(a) BENEFICIAL OWNERSHIP REPORTING COMPLIANCE. Section 16(a) of
the Securities Exchange Act of 1934 requires Kroll-O'Gara's executive officers
and directors, and persons who beneficially own more than ten percent of
Kroll-O'Gara's equity securities, to file reports of security ownership and
changes in that ownership with the Securities and Exchange Commission. These
persons also are required by SEC regulations to furnish Kroll-O'Gara with copies
of all Section 16(a) forms they file. Based upon a review of copies of these
forms and written representations from its executive officers and directors,
Kroll-O'Gara believes that all Section 16(a) forms were filed on a timely basis
during and for 1998, except that a Form 4 reporting shares sold was filed after
its due date by Mr. Cherkasky and amended Forms 5 are being filed after their
due date by Messrs. Cogan, Ritter, Sessions and Smith reporting phantom stock
units credited under Kroll-O'Gara's new Outside Directors' Deferred
Compensation Plan.
 
                                     -4-
<PAGE>   5
 
ITEM 11. EXECUTIVE COMPENSATION

     SUMMARY INFORMATION. The following table sets forth, for the fiscal years
indicated, amounts of cash and certain other compensation paid by Kroll-O'Gara
and its subsidiaries, for services in all capacities, to Jules B. Kroll,
Kroll-O'Gara's Chief Executive Officer, and each of the four other most highly
compensated executive officers during 1998. These persons are sometimes referred
to as the "named executive officers."
 
                           SUMMARY COMPENSATION TABLE
 
<TABLE>
<CAPTION>
                                                                     LONG TERM
                                   ANNUAL COMPENSATION          COMPENSATION AWARDS
                                --------------------------   -------------------------
                                                    OTHER                  SECURITIES
                                                   ANNUAL    RESTRICTED    UNDERLYING
                                                   COMPEN-     STOCK      STOCK OPTION    ALL OTHER
       NAME AND                 SALARY    BONUS    SATION      AWARDS        GRANTS      COMPENSATION
  PRINCIPAL POSITION     YEAR     ($)      ($)       ($)        ($)           (#)            ($)
-----------------------  ----   -------   ------   -------   ----------   ------------   ------------
<S>                      <C>    <C>       <C>      <C>       <C>          <C>            <C>
Jules B. Kroll(1)        1998   375,000       --      --         --              --         31,915(2)
Chairman and Chief       1997   489,583       --      --         --              --         32,965
Executive Officer        1996   500,000   75,000      --         --              --         31,715

Thomas M. O'Gara         1998   275,000       --      --         --              --          3,909(3)
Vice Chairman            1997   252,083       --      --         --          23,150          4,568
                         1996   379,081    7,000      --         --              --          4,912

Wilfred T. O'Gara        1998   350,000      --       --         --              --          2,292(3)
President and Chief      1997   240,000   45,000      --         --          98,150          4,898
Operating Officer        1996   200,231   45,000      --         --          17,000          4,240

Michael G. Cherkasky(1)  1998   400,000       --      --         --              --         25,930(2)
Chief Operating
  Officer --             1997   400,000       --      --         --          25,000         28,914
Investigations and       1996   300,000   75,000     898         --          68,647         26,767
Intelligence Group

Michael J. Lennon        1998   185,000   74,000      --         --              --          2,237(3)
Chief Operating
  Officer --             1997   148,333   70,000      --         --          20,000          5,401
Security Products and    1996   128,334   60,317      --         --          17,000          4,258
Services Group

Nazzareno E.
  Paciotti(1)            1998   275,520   66,667      --         --              --         19,813(2)
Chief Financial Officer  1997   275,520   66,667      --         --          15,000         26,984
                         1996   225,520   50,000      --         --          68,647         24,984
</TABLE>
 
---------------
(1) Messrs. Kroll, Cherkasky and Paciotti were unaffiliated with Kroll-O'Gara
    prior to the merger with Kroll Holdings in December 1997; however, their
    compensation information is given on a pooling of interests basis, as if
    they had been executive officers of Kroll-O'Gara throughout the periods
    presented.
(2) Represents pension contributions of $14,000 for Mr. Kroll, $16,000 for Mr.
    Cherkasky and $9,662 for Mr. Paciotti as well as profit-sharing
    contributions of $500 for each person, supplemental disability plan benefits
    of $12,465 for Mr. Kroll, $7,516 for Mr. Cherkasky and $6,483 for Mr.
    Paciotti and group term life insurance benefits of $4,950 for Mr. Kroll,
    $1,914 for Mr. Cherkasky and $3,168 for Mr. Paciotti.
(3) Represents profit-sharing contributions to the Company's 401(k) Plan of
    $2,691 for Mr. Thomas M. O'Gara, $1,578 for Mr. Wilfred T. O'Gara and $1,747
    for Mr. Lennon as well as executive disability insurance plan benefits of
    $1,218 for Mr. Thomas M. O'Gara, $714 for Mr. Wilfred T. O'Gara and $490 for
    Mr. Lennon.
 
     EMPLOYMENT AGREEMENTS. Commencing December 1, 1997, Kroll-O'Gara has
employment agreements, or amendments to existing employment agreements, which
expire on November 30, 2000, with each of its executive officers except Mr.
Cherkasky providing for annual base salaries in the following amounts: Jules B.
Kroll, $375,000; Thomas M. O'Gara, $275,000; Wilfred T. O'Gara, $350,000;
Michael J. Lennon, $185,000; Nazzareno E. Paciotti, $275,000; Nicholas P.
Carpinello, $180,000; Abram S. Gordon, $150,000. Each
 
                                     -5-
<PAGE>   6
 
executive officer, including Mr. Cherkasky, also is entitled to participate in
an annual bonus plan established by the Compensation Committee of the Board of
Directors and to receive up to 50% of his bonus in shares of Kroll-O'Gara's
common stock. Pursuant to these employment agreements, employment may be
terminated by Kroll-O'Gara at any time with or without cause, except that, in a
case of termination without cause, the employee is entitled to receive
compensation for the greater of the balance of the term of the agreement or one
year. The agreements also provide that if Kroll-O'Gara does not renew the
agreement for one year or more at the end of the term, the employee will receive
an amount equal to one year's base salary. Each employment agreement restricts
the executive officer from competing with Kroll-O'Gara during the term of the
agreement, and for two years thereafter if termination of employment is for
cause or at the volition of the employee. Each of Messrs. Thomas M. and Wilfred
T. O'Gara has further agreed that during his employment and for a period of 10
years thereafter he will not directly or indirectly own any interest in or
perform any services for any entity which uses the word "O'Gara" as a business
or trade name and competes with Kroll-O'Gara. Additionally, Mr. Kroll has agreed
that during his employment and for a period of 10 years thereafter he will not
directly or indirectly own any interest in or perform any services for any
entity which uses the word "Kroll" as a business or trade name and competes with
Kroll-O'Gara.
 
     STOCK OPTIONS. No stock options were granted to the named executive
officers during 1998. With respect to each named executive officer, the
following table sets forth information concerning stock options exercised during
1998 and unexercised stock options held at December 31, 1998.
 
                AGGREGATED OPTION EXERCISES IN LAST FISCAL YEAR
                            AND FY-END OPTION VALUES
 
<TABLE>
<CAPTION>
                                                                      NUMBER OF
                                                                     SECURITIES          VALUE OF
                                                                     UNDERLYING         UNEXERCISED
                                                      VALUE          UNEXERCISED       IN-THE-MONEY
                                                   REALIZED ($)      OPTIONS AT         OPTIONS AT
                                                 ----------------    FY-END (#)         FY-END ($)
                                                 (MARKET PRICE ON   -------------   -------------------
                               SHARES ACQUIRED    EXERCISE LESS     EXERCISABLE/       EXERCISABLE/
            NAME               ON EXERCISE (#)   EXERCISE PRICE)    UNEXERCISABLE      UNEXERCISABLE
            ----               ---------------   ----------------   -------------   -------------------
<S>                            <C>               <C>                <C>             <C>
Jules B. Kroll...............          --                 --                   --                    --
Thomas M. O'Gara.............          --                 --         7,716/15,434       210,940/421,935
Wilfred T. O'Gara............       5,000             77,500        44,716/65,434   1,139,384/1,548,312
Michael G. Cherkasky.........          --                 --        98,862/16,667     3,450,378/369,807
Michael J. Lennon............       5,365             98,582        18,301/13,334       512,464/316,692
Nazzareno E. Paciotti........          --                 --        95,529/10,000     3,376,425/221,880
</TABLE>
 
DIRECTORS' COMPENSATION
 
     Directors who are not employees of Kroll-O'Gara receive annually a $15,000
fee, plus options to purchase 2,000 shares of common stock, for serving as
directors. These directors also are paid $1,000 for each Board of Directors
meeting attended in person and $750 for Board meetings held by telephone. Each
committee Chairman receives an annual fee of $1,600 and committee members,
including the Chairman, receive $750 per meeting attended, whether in person or
by telephone, unless the meeting occurs on the same day as a Board meeting, in
which case no separate fee is paid. Employee directors are not separately
compensated for their services as directors.

     Under Kroll-O'Gara's Outside Directors' Deferred Compensation Plan, each
nonemployee director is entitled to defer all or a portion of his director's
fee into a bookkeeping account. The account is credited with "phantom"
Kroll-O'Gara common stock units equivalent in value to the amount of each fee
deferred, at the time earned. Unless a later time is selected by a director,
the value of the units in the director's account will be paid in cash when the
director's service on Kroll-O'Gara's Board terminates or at the time of a
"change in control" of Kroll-O'Gara as defined in the Plan.

                                     -6-
<PAGE>   7
 
ITEM 12. SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT
 
     The following table sets forth certain information regarding the beneficial
ownership of Kroll-O'Gara's common stock on March 31, 1999 by each beneficial
owner of more than five percent of the common stock, each director and each
named executive officer individually and all directors and executive officers as
a group. Unless otherwise indicated, all shares are owned directly and the
indicated owner has sole voting and dispositive power with respect to such
shares.
 
<TABLE>
<CAPTION>
                                                                  BENEFICIAL
                                                                 OWNERSHIP(1)
                                                              -------------------
                            NAME                               NUMBER     PERCENT
                            ----                              ---------   -------
<S>                                                           <C>         <C>
Jules B. Kroll(2)(3)........................................  2,879,991    13.8
Thomas M. O'Gara(2).........................................  2,433,652    11.7
Wilfred T. O'Gara...........................................    280,772     1.3
Michael G. Cherkasky........................................    127,272       *
Marshall S. Cogan...........................................         --      --
Michael J. Lennon...........................................     25,434       *
Raymond E. Mabus............................................      2,000       *
Nazzareno E. Paciotti.......................................    108,845       *
Hugh E. Price...............................................      8,889       *
Jerry E. Ritter.............................................      2,000       *
William S. Sessions.........................................      2,000       *
Howard I. Smith(2)(4).......................................  1,444,212     6.9
All directors and executive officers as a group
(14 persons)(5).............................................  7,401,365    35.0
American International Group, Inc.(2).......................  1,444,212     6.9
</TABLE>
 
---------------
 *  Less than 1%.
(1) Included in the shares listed are the following numbers of shares of common
    stock which may be acquired through the exercise of currently exercisable
    stock options or stock options which become exercisable within 60 days after
    March 31, 1999; Mr. Kroll, none; Mr. Thomas M. O'Gara, 15,433 shares; Mr.
    Wilfred T. O'Gara, 37,730 shares; Mr. Cherkasky, 98,862 shares; Mr. Cogan,
    none; Mr. Lennon, 14,636 shares; Mr. Mabus, 2,000 shares; Mr. Paciotti,
    95,529 shares; Mr. Price, 8,889 shares; Mr. Ritter, 1,000 shares; Mr.
    Sessions, 2,000 shares; Mr. Smith, none; and all directors and executive
    officers as a group, 305,411 shares.
(2) Mr. Kroll's address is 900 Third Avenue, New York, New York 10022. Mr.
    O'Gara's address is 9113 LeSaint Drive, Fairfield, Ohio 45014. Mr. Smith's
    and AIG's address is 70 Pine Street, New York, New York 10270.
(3) Does not include 192,560 shares held by trusts for the benefit of Mr.
    Kroll's adult children, in which Mr. Kroll disclaims any beneficial
    interest.
(4) Consists of 1,444,212 shares held by AIG. Mr. Smith disclaims any beneficial
    interest in these shares.
(5) Includes 1,444,212 shares held by AIG which are deemed to be owned by Mr.
    Smith and in which he disclaims any beneficial interest.
 
ITEM 13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS
 
     In connection with Kroll-O'Gara's initial public offering, the Board of
Directors adopted a policy requiring that any future transactions, including
loans, between Kroll-O'Gara and its officers, directors, principal shareholders
and their affiliates be on terms no less favorable to Kroll-O'Gara than could be
obtained from unrelated third parties and that any such transactions be approved
by a majority of the disinterested members of the Board of Directors.
 
                                     -7-
<PAGE>   8
 
     Described below are certain transactions and relationships between
Kroll-O'Gara and its officers, directors and shareholders which have occurred
during the last fiscal year. Except with respect to interest rates charged on
certain of the intercompany notes and accounts payable/receivable, Kroll-O'Gara
believes that the material terms of the various transactions were as favorable
as could have been obtained from unrelated third parties.
 
VICTORY AVIATION
 
     Victory Aviation Services, Inc. is a Delaware corporation of which Messrs.
Thomas M. O'Gara, Wilfred T. O'Gara and Carpinello own approximately 92%, 1% and
1%, respectively, of the outstanding capital stock.
 
     LEASE AGREEMENTS. Kroll-O'Gara has a Master Equipment Lease with Victory
Aviation, entered into in July 1995, under which Kroll-O'Gara leases various
items of equipment from Victory Aviation. As of December 31, 1998, Kroll-O'Gara
had approximately $1,250,000 of equipment under lease for terms up to 36 months,
beginning on various dates between July 1995 and April 1996. Rental expenses
were $396,005 for the year ended December 31, 1998.
 
     SUPPLIER ARRANGEMENTS. During 1995 and 1996, Kroll-O'Gara purchased the
dual-hard steel required for its vehicle armoring from Victory Aviation, which
distributed the steel for an unrelated third party. At December 31, 1998,
Kroll-O'Gara had receivables of $282,345 from Victory Aviation in connection
with the prior arrangement, which sum is guaranteed by the shareholders of
Victory Aviation. All other aspects of the arrangement have been terminated.
 
     CORPORATE AIRCRAFT. In February 1995, Kroll-O'Gara entered into a lease for
a Gulfstream G-II aircraft owned by Victory Aviation. Effective June 1, 1998, 
Kroll-O'Gara reached an agreementto amend the corporate aircraft lease. 
The terms of the aircraft lease addendumprovide Kroll-O'Gara with a hourly
discount from the normal commercial hourlyrate on future charters of corporate
aircrafts from Victory Aviation in order toamortize the remaining portion of
existing lease deposits from the originalaircraft lease. Kroll-O'Gara had
approximately $484,000 in unamortized leasedeposits with Victory Aviation
as of December 31, 1998. Rental expense related to the Gulfstrean lease, 
including amortization of the deposit, was $292,000 in 1998.
 
     In 1998, Kroll-O'Gara paid Victory Aviation $296,000 relating to use of the
G-II aircraft during the roadshow for a stock offering and $270,000 relating to
use of another corporate aircraft in connection with the merger with Securify.
Kroll-O'Gara believes that the rate paid was equivalent to that charged by
Victory Aviation to other unrelated companies for similar services during 1998
and compared favorably to rates charged by another unrelated charter service for
similar aircraft.
 
INTERCOMPANY NOTES AND ACCOUNTS PAYABLE/RECEIVABLE AND CERTAIN LOANS
 
     In 1998, Mr. Thomas M. O'Gara repaid a $120,191 advance made by OHE prior
to Kroll-O'Gara's initial public offering. This amount was not represented by a
promissory note. Also in 1998, Mr. Kroll was repaid $332,490 in principal and
interest owed him on a promissory note issued by a subsidiary of Kroll Holdings
at the time of the merger into Kroll-O'Gara. There were no principal payments
made with respect to this note prior to 1998. During 1998, Kroll-O'Gara and
Messrs. Thomas M. O'Gara and Kroll agreed to reimburse Kroll-O'Gara for a
portion of general and administrative expenses, including outside professional
fees, office rent and travel expenses, which were incurred for the benefit of
both Kroll-O'Gara and the individuals. Amounts due to Kroll-O'Gara at December
31, 1998 pursuant to this agreement were $429,953 from Mr. Thomas M. O'Gara and,
after repayment of the promissory note referred to above, $85,672 from Mr.
Kroll.
 
     During 1998, Kroll-O'Gara rendered risk management services, including
marketing support, and claims investigations services to AIG and its
subsidiaries. Kroll-O'Gara billed AIG and its subsidiaries $4,877,478 in 1998
for these services. The year-end accounts receivable balance for AIG was
$1,290,558 at December 31, 1998. Since 1995, Kroll-O'Gara has purchased some of
its liability insurance, including Professional Errors
 
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<PAGE>   9
 
and Omissions and Directors and Officers liability insurance, from AIG's
subsidiaries. AIG's subsidiaries billed Kroll-O'Gara $474,800 for this insurance
during 1998. Kroll-O'Gara obtains the coverage through an independent insurance
broker and where possible obtains competitive proposals from unrelated third
parties.
 
BUILDING LEASE
 
     OLG, Limited, an Ohio limited liability company of which Messrs. Thomas M.
O'Gara, Wilfred T. O'Gara, Carpinello and Lennon own approximately 91%, 5%, 1%
and 1% of the outstanding capital stock, was formed in March 1996 for the
purpose of acquiring and leasing to Kroll-O'Gara a facility located at 4175
Muhlhauser Road, Fairfield, Ohio. OLG sold the building in August 1998. Total
lease payments made in 1998 by Kroll-O'Gara to OLG, prior to its sale of the
building, were $150,837.
 
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<PAGE>   10
 
                                   SIGNATURES
 
     Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the registrant has duly caused this amended report to be
signed on its behalf by the undersigned, thereunto duly authorized, as of the
28th day of April, 1999.
 
                                          THE KROLL-O'GARA COMPANY
 
                                          By /s/ NICHOLAS P. CARPINELLO
                                            ------------------------------------
                                             Nicholas P. Carpinello
                                             Controller and Treasurer
 
 
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