<PAGE>   1
                                                                   Exhibit 10(a)
                                                                   -------------

                                  $400,000,000

                                  $700,000,000

                                  $750,000,000

                                  $550,000,000





                                    TRW INC.


                              6 1/2% Notes Due 2002

                              6 5/8% Notes Due 2004

                              7 1/8% Notes Due 2009

                           7 3/4% Debentures Due 2029






                               PURCHASE AGREEMENT




                                  May 26, 1999


<PAGE>   2



                                                                    May 26, 1999


Morgan Stanley & Co. Incorporated
J.P. Morgan Securities Inc.
Salomon Smith Barney Inc.,
as representatives of the Initial Purchasers
named in Schedule II hereto
c/o Morgan Stanley & Co. Incorporated
     1585 Broadway
     New York, New York 10036

Dear Sirs and Mesdames:

                  TRW Inc., an Ohio corporation (the "COMPANY"), proposes to
issue and sell to the several purchasers named in Schedule II hereto (the
"INITIAL PURCHASERS"), for whom you (the "Representatives") are acting as
representatives, $400,000,000 principal amount of its 6 1/2% Notes Due 2002,
$700,000,000 principal amount of its 6 5/8% Notes Due 2004, $750,000,000
principal amount of its 7 1/8% Notes Due 2009, and $550,000,000 principal amount
of its 7 3/4% Debentures Due 2029 (collectively, the "SECURITIES"), to be issued
pursuant to the provisions of an Indenture dated as of May 1, 1986 (as
supplemented, the "INDENTURE"), as supplemented by the First Supplemental
Indenture dated as of August 24, 1989, the Second Supplemental Indenture dated
as of June 2, 1999, the Third Supplemental Indenture dated as of June 2, 1999,
the Fourth Supplemental Indenture dated as of June 2, 1999, and the Fifth
Supplemental Indenture dated as of June 2, 1999, between the Company and The
Chase Manhattan Bank, as successor Trustee (the "TRUSTEE") to Mellon Bank N.A.

                  The Securities will be offered and sold without being
registered under the Securities Act of 1933, as amended (the "SECURITIES ACT"),
to qualified institutional buyers in compliance with the exemption from
registration provided by Rule 144A under the Securities Act, in offshore
transactions in reliance on Regulation S under the Securities Act ("REGULATION
S") and to institutional accredited investors (as defined in Rule 501(a)(1),
(2), (3) or (7) under the Securities Act) that deliver a letter in the form
annexed to the Final Memorandum (as defined below).

In connection with the sale of the Securities, the Company has prepared a
preliminary offering memorandum (the "PRELIMINARY MEMORANDUM") and will prepare
a final offering memorandum (the "FINAL MEMORANDUM" and, with the Preliminary
Memorandum, each a "MEMORANDUM") including or incorporating by reference a
description of the terms of the Securities, the terms of the offering and a
description of the Company. The Company hereby confirms that it has authorized
the use of each Memorandum in connection with the offering and resale of the
Securities by the Initial Purchasers, subject to their obligations hereunder. As
used herein, the term "Memorandum" shall include in each case the documents
incorporated by reference therein. The terms "SUPPLEMENT", "AMENDMENT"
and "AMEND" as used herein with

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respect to a Memorandum shall include all documents deemed to be incorporated by
reference in the Preliminary Memorandum or Final Memorandum that are filed
subsequent to the date of such Memorandum with the Securities and Exchange
Commission (the "COMMISSION") pursuant to the Securities Exchange Act of 1934,
as amended (the "EXCHANGE ACT").

                  The Initial Purchasers and their direct and indirect permitted
transferees will be entitled to the benefits of the Registration Rights
Agreement dated the date hereof between the Company and the Initial Purchasers
(the "Registration Rights Agreement"), pursuant to which the Company will file a
registration statement or registration statements (each, a "Registration
Statement") with the Commission registering the Securities and/or the Exchange
Securities (as defined in the Registration Rights Agreement) under the
Securities Act.

         1. Representations and Warranties. The Company represents and warrants
to, and agrees with, each Initial Purchaser as set forth below in this Section
1:

                  (a) Each document, if any, filed or to be filed pursuant to
         the Exchange Act and incorporated by reference in either Memorandum
         complied or will comply when so filed in all material respects with the
         Exchange Act and the rules and regulations thereunder and when read
         together and with the other information in the Preliminary Memorandum
         does not contain and the Final Memorandum, in the form used by the
         Initial Purchasers to confirm sales and on the Closing Date (as defined
         in Section 4), will not contain an untrue statement of a material fact
         or omit to state a material fact required to be stated therein or
         necessary to make the statements therein, in the light of the
         circumstances under which they were made, not misleading.

                  (b) Any documents filed by the Company under the Exchange Act
         that are incorporated by reference (in whole or in part) in either
         Memorandum or that are incorporated by reference (in whole or in part)
         in a Registration Statement, as of the dates they were filed or
         hereafter are with the Commission, complied and will comply as to form
         in all material respects with the requirements of the Exchange Act and
         the rules and regulations of the Commission thereunder (the "Exchange
         Act Regulations").

                  (c) When the Securities are issued and delivered pursuant to
         this Agreement, such securities will not be of the same class (within
         the meaning of Rule 144A) as securities of the Company which are listed
         on a national securities exchange registered under Section 6 of the
         Exchange Act or quoted in a U.S. automated interdealer quotation
         system.

                  (d) The Company has been duly incorporated and is validly
         existing as a corporation in good standing under the laws of Ohio, with
         corporate power and authority to own, lease and operate its properties
         and to conduct its business as described in each Memorandum and is duly
         qualified as a foreign corporation to transact business in each
         jurisdiction in which the conduct of its business or its ownership or
         leasing of property requires such qualification, except to the extent

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         that the failure to be so qualified would not have a material adverse
         effect on the financial condition or earnings, business affairs or
         business prospects of the Company and its subsidiaries, taken as a
         whole; and the Company is in good standing in the State of California
         and the Commonwealth of Virginia.

                  (e) (if the Company has one or more Significant Subsidiaries
         as of the date hereof and as of the Closing Date) each Significant
         Subsidiary of the Company has been duly incorporated, is validly
         existing as a corporation in good standing under the laws of the
         jurisdiction of its incorporation, has the corporate power and
         authority to own, lease and operate its property and to conduct its
         business as described in each Memorandum and is duly qualified to
         transact business and is in good standing in each jurisdiction in which
         the conduct of its business or its ownership or leasing of property
         requires such qualification, except to the extent that the failure to
         be so qualified or be in good standing would not have a material
         adverse effect on the financial condition, or the earnings, business
         affairs or business prospects of the Company and its subsidiaries,
         taken as a whole; all of the issued shares of capital stock of each
         Significant Subsidiary of the Company held by the Company have been
         duly and validly authorized and issued, are fully paid and
         non-assessable and are owned directly or indirectly by the Company,
         free and clear of all liens, encumbrances, equities or claims. For
         purposes of this paragraph a "Significant Subsidiary" shall mean a
         "significant subsidiary" as defined in Rule 405 of Regulation C under
         the Act.

                  (f) This Agreement has been duly authorized, executed and
         delivered by the Company.

                  (g) The Securities have been duly authorized and, when
         executed and authenticated in accordance with the provisions of the
         Indenture and delivered to and paid for by the Initial Purchasers in
         accordance with the terms of this Agreement, will constitute valid and
         legally binding obligations of the Company enforceable in accordance
         with their terms, except as enforcement thereof may be limited by
         bankruptcy, insolvency or other laws relating to or affecting
         enforcement of creditors' rights or by general equity principles, and
         except further as enforcement thereof may be limited by (i)
         requirements that a claim with respect to any Securities denominated
         other than in United States dollars (or a foreign currency or currency
         unit judgment in respect of such claim) be converted into United States
         dollars at a rate of exchange prevailing on a date determined pursuant
         to applicable law or (ii) governmental authority to limit, delay or
         prohibit the making of payments in a foreign currency or currency units
         or payments outside the United States; the Securities and the Indenture
         will be substantially in the form heretofore delivered to the Initial
         Purchasers and conform in all material respects to all statements
         relating thereto contained in the Final Memorandum; and the Securities
         will be entitled to the benefits provided by the Indenture.

                  (h) Each of the Indenture and the Registration Rights
         Agreement has been duly authorized, executed and delivered by, and is a
         valid and legally binding agreement of, the Company enforceable in
         accordance with its terms, except as enforcement thereof may be limited
         by bankruptcy, insolvency or other laws



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         relating to or affecting enforcement of creditors' rights or by general
         equity principles and except as rights to indemnification and
         contribution under the Registration Rights Agreement may be limited
         under applicable law. The Registration Rights Agreement will conform in
         all material respects to the description thereof, if any, to be
         contained in either Memorandum.

                  (i) The execution and delivery by the Company of, and the
         performance by the Company of its obligations under, this Agreement,
         the Indenture, the Registration Rights Agreement and the Securities
         will not contravene any provision of applicable law or constitute a
         default under the Amended Articles of Incorporation of the Company or
         by-laws of the Company or any indenture, other agreement or instrument
         binding upon the Company or any of its subsidiaries that is material to
         the Company and its subsidiaries, taken as a whole, or any judgment,
         order or decree of any governmental body, agency or court having
         jurisdiction over the Company or any subsidiary, and no consent,
         approval, authorization or order of, or qualification with, any court
         or governmental body or agency is required for the performance by the
         Company of its obligations under this Agreement, the Indenture, the
         Securities or the Registration Rights Agreement, except such as may be
         required by the securities or Blue Sky laws of the various states in
         connection with the offer and sale of the Securities.

                  (j) Except as may be set forth in either Memorandum, there is
         no action, suit or proceeding before or by any court or governmental
         agency or body, domestic or foreign, now pending, against or affecting,
         the Company or any of its subsidiaries, which might, in the opinion of
         the Company, result in any material adverse change in the financial
         position of the Company and its subsidiaries taken as a whole, or might
         materially and adversely affect the assets of the Company and its
         subsidiaries, taken as a whole.

                  (k) The Company is not, and after giving effect to the
         offering and sale of the Securities and the application of the proceeds
         thereof as described in the Final Memorandum, will not be an
         "investment company" as such term is defined in the Investment Company
         Act of 1940, as amended.

                  (l) Neither the Company nor any affiliate (as defined in Rule
         501(b) of Regulation D under the Securities Act, an "AFFILIATE") of the
         Company has directly, or through any agent, (i) sold, offered for sale,
         solicited offers to buy or otherwise negotiated in respect of, any
         security (as defined in the Securities Act) which is or will be
         integrated with the sale of the Securities in a manner that would
         require the registration under the Securities Act of the Securities or
         (ii) engaged in any form of general solicitation or general advertising
         in connection with the offering of the Securities, (as those terms are
         used in Regulation D under the Securities Act) or in any manner
         involving a public offering within the meaning of Section 4(2) of the
         Securities Act; provided, however, the Company makes no representations
         with respect to the activities of the Initial Purchasers.

                  (m) None of the Company, its Affiliates or any person acting
         on its or their behalf has engaged or will engage in any directed
         selling efforts (within the



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         meaning of Regulation S) with respect to the Securities and the Company
         and its Affiliates and any person acting on its or their behalf have
         complied and will comply with the offering restrictions requirement of
         Regulation S; provided, however, the Company makes no representations
         with respect to the activities of the Initial Purchasers.

                  (n) It is not necessary in connection with the offer, sale and
         delivery of the Securities to the Initial Purchasers in the manner
         contemplated by this Agreement to register the Securities under the
         Securities Act or to qualify any indenture in respect of the Securities
         under the Trust Indenture Act of 1939, as amended (the "Trust Indenture
         Act").

                  (o) The Securities satisfy the requirements set forth in Rule
         144A(d)(3) under the Securities Act.

                  (p) The financial statements of the Company and its
         consolidated subsidiaries included or incorporated by reference in
         either Memorandum present fairly the consolidated financial position of
         the Company and its consolidated subsidiaries as at the dates indicated
         and the consolidated results of their operations for the periods
         specified; and except as stated therein, said financial statements have
         been prepared in conformity with generally accepted accounting
         principles in the United States applied on a consistent basis.

                  2. Agreements to Sell and Purchase. The Company hereby agrees
to sell to the several Initial Purchasers, and each Initial Purchaser, upon the
basis of the representations and warranties herein contained, but subject to the
conditions hereinafter stated, agrees, severally and not jointly, to purchase
from the Company at the purchase price for the Securities set forth in Schedule
I hereto, the respective principal amount of Securities set forth opposite such
Initial Purchaser's name in Schedule II hereto.

                  3. Terms of Offering. You have advised the Company that the
Initial Purchasers will make an offering of the Securities purchased by the
Initial Purchasers hereunder on the terms to be set forth in the Final
Memorandum, as soon as practicable after this Agreement is entered into as in
your judgment is advisable.

                  4. Payment and Delivery. Payment for the Securities shall be
made to the Company in Federal or other funds immediately available in New York
City against delivery of such Securities for the respective accounts of the
several Initial Purchasers at 10:00 a.m., New York City time, on June 2, 1999,
or at such other time on the same or such other date, not later than June 9,
1999, as shall be designated in writing by you. The time and date of such
payment are hereinafter referred to as the "CLOSING DATE."

                  Certificates for the Securities shall be in definitive form or
global form, as specified by you, and registered in such names and in such
denominations as you shall request in writing not later than one full business
day prior to the Closing Date. The certificates evidencing the Securities shall
be delivered to you on the Closing Date for the respective accounts of the
several Initial Purchasers, with any transfer taxes payable in connection with
the transfer of the Securities to the Initial Purchasers duly paid, against



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payment of the Purchase Price therefor plus accrued interest, if any, to the
date of payment and delivery.

                  5. Conditions to the Initial Purchasers' Obligations. The
several obligations of the Initial Purchasers to purchase and pay for the
Securities on the Closing Date shall be subject to the accuracy of the
representations and warranties on the part of the Company contained herein as of
the date hereof, and as of the Closing Date, to the accuracy of the statements
of the Company made in any certificates pursuant to the provisions hereof, to
the performance by the Company of its obligations hereunder, to the due
execution and delivery of the Indenture and to the following additional
conditions:

                  (a) The Initial Purchasers shall have received on the Closing
         Date a certificate, dated the Closing Date and signed by an executive
         officer of the Company, to the effect that the representations and
         warranties of the Company contained in this Agreement are true and
         correct in all material respects as of the Closing Date with the same
         effect as if made on the Closing Date and that the Company has complied
         with all of the agreements and satisfied all of the conditions on its
         part to be performed or satisfied hereunder on or before the Closing
         Date and that, subsequent to the date of most recent financial
         statements in the Final Memorandum, there has been no material adverse
         change in the condition (financial or other), earnings, business or
         properties of the Company and its subsidiaries taken as a whole,
         whether or not arising from transactions in the ordinary course of
         business, except as set forth in or contemplated by the Final
         Memorandum or as described in such certificate.

                  (b) The Initial Purchasers shall have received on the Closing
         Date an opinion of the General Counsel or an Assistant General Counsel
         of the Company, dated the Closing Date, to the effect set forth in
         Exhibit A.

                  (c) The Initial Purchasers shall have received on the Closing
         Date an opinion of Cravath, Swaine & Moore, counsel for the Initial
         Purchasers, dated the Closing Date, to the effect set forth in Exhibit
         B.

                  (d) The Initial Purchasers shall have received on the Closing
         Date a letter, dated the Closing Date in form and substance
         satisfactory to the Initial Purchasers, from each of (i) Ernst & Young
         LLP, independent public accountants, (ii) KPMG Audit plc, independent
         public accountants, (iii) KPMG Audit plc and Ernst & Young, jointly,
         and (iv) Ernst & Young, independent public accountants, in each case
         containing statements and information of the type ordinarily included
         in accountants' "comfort letters" to underwriters with respect to the
         financial statements and certain financial information contained in or
         incorporated by reference into the Final Memorandum; provided that (A)
         the Ernst & Young LLP letter delivered on the Closing Date shall use a
         "cut-off date" not earlier than the date hereof and (B) the KPMG Audit
         plc letter delivered on the Closing Date shall use a "cut-off date" not
         earlier than March 24, 1999.



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                  (e) Subsequent to the execution of this Agreement, there shall
         not have been any decrease in the ratings of any of the Company's debt
         securities by Moody's Investors Service, Inc. or Standard & Poor's
         Corporation.

                  (f) Prior to the Closing Date, the Company shall have
         furnished to the Initial Purchasers such further information,
         certificates and documents as the Representatives may reasonably
         request.

                  (g) The Registration Rights Agreement shall have been duly
         authorized, executed and delivered by the Company, the Indenture shall
         have been duly authorized, executed and delivered by the Company, all
         the covenants and agreements contained herein to be fulfilled or
         complied with by the Company at or prior to such Closing Date shall
         have been duly performed, fulfilled or complied with in all material
         respects.

                  If any of the conditions specified in this Section 5 shall not
have been fulfilled in all material respects when and as provided in this
Agreement, or if any of the opinions and certificates mentioned above or
elsewhere in this Agreement shall not be in all material respects reasonably
satisfactory in form and substance to the Initial Purchasers and counsel for the
Initial Purchasers, this Agreement and all obligations of the Initial Purchasers
hereunder may be canceled at, or at any time prior to, the Closing Date by the
Initial Purchasers. Notice of such cancelation shall be given to the Company in
writing or by telephone or telegraph confirmed in writing.

                  6. Covenants of the Company. In further consideration of the
agreements of the Initial Purchasers contained in this Agreement, the Company
covenants with each Initial Purchaser as follows:

                  (a) To furnish to you in New York City, without charge, prior
         to 10:00 a.m., New York City time, on the business day next succeeding
         the date of this Agreement and during the period mentioned in Section
         6(c), as many copies of the Final Memorandum, any documents
         incorporated by reference therein and any supplements and amendments
         thereto as you may reasonably request. The Company will pay the
         expenses of printing all documents relating to the offering.

                  (b) The Company will advise the Initial Purchasers promptly of
         any proposal to amend or supplement either Memorandum and will afford
         the Initial Purchasers a reasonable opportunity to comment on any such
         proposed amendment or supplement. The Company will not file any
         document under the Exchange Act before the completion of the offering
         of the Securities by the Initial Purchasers if such document would be
         incorporated by reference in either Memorandum and if the filing of
         such document would cause either Memorandum, as amended or supplemented
         by the filing of such document, to contain an untrue statement of a
         material fact or to omit to state a material fact necessary to make the
         statements therein, in light of the circumstances under which they were
         made, not misleading.



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                  (c) If, during such period after the date hereof and prior to
         the date on which all of the Securities shall have been sold by the
         Initial Purchasers to purchasers who are not affiliates of such Initial
         Purchaser, any event occurs as a result of which the Final Memorandum
         as then amended (including, without limitation, any document
         incorporated by reference therein) would include any untrue statement
         of a material fact or omit to state any material fact necessary to make
         the statements therein, in the light of the circumstances under which
         they were made, not misleading, forthwith to prepare and furnish, at
         its own expense, to the Initial Purchasers, either amendments or
         supplements to the Final Memorandum which will correct such statement
         or omission or misstatement.

                  (d) To endeavor to qualify the Securities for offer and sale
         under the securities or Blue Sky laws of such jurisdictions as you
         shall reasonably request.

                  (e) Whether or not the transactions contemplated in this
         Agreement are consummated or this Agreement is terminated, to pay or
         cause to be paid all expenses incident to the performance of its
         obligations under this Agreement, including: (i) the fees,
         disbursements and expenses of the Company's counsel and the Company's
         accountants in connection with the issuance and sale of the Securities
         and all other fees or expenses in connection with the preparation of
         each Memorandum and all amendments and supplements thereto, including
         all printing costs associated therewith, and the delivering of copies
         thereof to the Initial Purchasers, in the quantities herein above
         specified, (ii) all costs and expenses related to the transfer and
         delivery of the Securities to the Initial Purchasers, including any
         transfer or other taxes payable thereon, (iii) the cost of printing or
         producing any Blue Sky memorandum in connection with the offer and sale
         of the Securities under state securities laws and all expenses in
         connection with the qualification of the Securities for offer and sale
         under state securities laws as provided in Section 6(d) hereof,
         including filing fees and the reasonable fees and disbursements of
         counsel for the Initial Purchasers in connection with such
         qualification and in connection with the Blue Sky memorandum, (iv) any
         fees charged by rating agencies for the rating of the Securities, (v)
         all document production charges and expenses of counsel to the Initial
         Purchasers (but not including their fees for professional services) in
         connection with the preparation of this Agreement, (vi) the costs and
         charges of the Trustee and any transfer agent, listing agent, registrar
         or depositary, (vii) the cost of the preparation, issuance and delivery
         of the Securities, (viii) the costs and expenses of the Company
         relating to investor presentations on any "road show" undertaken in
         connection with the marketing of the offering of the Securities,
         including, without limitation, expenses associated with the production
         of road show slides and graphics, fees and expenses of any consultants
         engaged in connection with the road show presentations with the prior
         approval of the Company, travel and lodging expenses of the
         representatives and officers of the Company and any such consultants,
         and the cost of any aircraft chartered in connection with the road
         show, and (ix) all other cost and expenses incident to the performance
         of the obligations of the Company hereunder for which provision is not
         otherwise made in this Section. It is understood, however, that except
         as provided in this Section, Section 8, and the last paragraph of
         Section 10, the Initial Purchasers will pay all of their costs and



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         expenses, including fees and disbursements of their counsel and
         transfer taxes payable on resale of any of the Securities by them.

                  (f) Neither the Company nor any Affiliate will sell, offer for
         sale or solicit offers to buy or otherwise negotiate in respect of any
         security (as defined in the Securities Act) which could be integrated
         with the sale of the Securities in a manner which would require the
         registration under the Securities Act of the Securities.

                  (g) Not to solicit any offer to buy or offer or sell the
         Securities by means of any form of general solicitation or general
         advertising (as those terms are used in Regulation D under the
         Securities Act) or in any manner involving a public offering within the
         meaning of Section 4(2) of the Securities Act.

                  (h) While any of the Securities remain "restricted securities"
         within the meaning of the Securities Act, to make available, upon
         request, to any seller of such Securities the information specified in
         Rule 144A(d)(4) under the Securities Act, unless the Company is then
         subject to Section 13 or 15(d) of the Exchange Act.

                  (i) None of the Company, its Affiliates or any person acting
         on its or their behalf (other than the Initial Purchasers) will engage
         in any directed selling efforts (as that term is defined in Regulation
         S) with respect to the Securities, and the Company and its Affiliates
         and each person acting on its or their behalf (other than the Initial
         Purchasers) will comply with the offering restrictions requirement of
         Regulation S.

                  (j) During the period from the Closing Date to the earlier of
         (i) two years after the Closing Date, or (ii) the date of effectiveness
         of a registration statement with respect to the Securities as
         contemplated in the Registration Rights Agreement, the Company will
         not, and will not permit any of its affiliates (as defined in Rule 144
         under the Securities Act) to, resell any of the Securities that have
         been reacquired by them, except for Securities purchased by the Company
         or any of its affiliates and resold in a transaction registered under
         the Securities Act.

                  (k) The Company will use its reasonable best efforts in
         cooperation with the Initial Purchasers to permit the Securities to be
         eligible for clearance and settlement through The Depository Trust
         Company.

                  (l) Each Security will bear the legends specified in the
         Indenture until, in the opinion of counsel of the Company, such legends
         are is no longer advisable because such Security is no longer subject
         to the restrictions on transfer described therein.

                  (m) For a period beginning at the time of execution of this
         Agreement and ending on the business day following the Closing Date,
         the Company will not, without the consent of Morgan Stanley & Co.
         Incorporated on behalf of the Initial Purchasers, offer, sell, contract
         to sell or otherwise dispose of any United States



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         dollar-denominated debt securities issued or guaranteed by the Company
         and having a maturity of more than 390 days from the date of issue.

                  7. Offering of Securities; Restrictions on Transfer. (a) Each
Initial Purchaser, severally and not jointly, represents and warrants that such
Initial Purchaser is a qualified institutional buyer as defined in Rule 144A
under the Securities Act (a "QIB") and an institutional accredited investor (as
defined below). Each Initial Purchaser, severally and not jointly, agrees with
the Company that (i) it will not solicit offers for, or offer or sell, such
Securities by any form of general solicitation or general advertising (as those
terms are used in Regulation D under the Securities Act) or in any manner
involving a public offering within the meaning of Section 4(2) of the Securities
Act and (ii) it will solicit offers for such Securities only from, and will
offer such Securities only to, persons that it reasonably believes to be (A) in
the case of offers inside the United States, (1) QIBs or (2) other institutional
accredited investors (as defined in Rule 501(a)(1), (2), (3) or (7) under the
Securities Act ("INSTITUTIONAL ACCREDITED INVESTORS") that, prior to their
purchase of the Securities, deliver to such Initial Purchaser a letter
containing the representations and agreements set forth in Appendix A to the
Memorandum and (B) in the case of offers outside the United States, to persons
other than U.S. persons ("FOREIGN PURCHASERS," which term shall include dealers
or other professional fiduciaries in the United States acting on a discretionary
basis for foreign beneficial owners (other than an estate or trust)) in reliance
upon Regulation S under the Securities Act that, in each case, in purchasing
such Securities are deemed to have represented and agreed as provided in the
Final Memorandum under the caption "Transfer Restrictions".

                  (b) Each Initial Purchaser, severally and not jointly,
represents, warrants, and agrees with respect to offers and sales outside the
United States that:

                  (i) such Initial Purchaser understands that no action has been
         or will be taken in any jurisdiction by the Company that would permit a
         public offering of the Securities, or possession or distribution of
         either Memorandum or any other offering or publicity material relating
         to the Securities, in any country or jurisdiction where action for that
         purpose is required;

                  (ii) such Initial Purchaser will comply with all applicable
         laws and regulations in each jurisdiction in which it acquires, offers,
         sells or delivers Securities or has in its possession or distributes
         either Memorandum or any such other material, in all cases at its own
         expense;

                  (iii) the Securities have not been registered under the
         Securities Act and may not be offered or sold within the United States
         or to, or for the account or benefit of, U.S. persons except in
         accordance with Rule 144A or Regulation S under the Securities Act or
         pursuant to another exemption from the registration requirements of the
         Securities Act;

                  (iv) such Initial Purchaser has offered the Securities and
         will offer and sell the Securities (A) as part of their distribution at
         any time and (B) otherwise until 40 days after the later of the
         commencement of the offering and the Closing Date,



                                       11
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         only in accordance with Rule 903 of Regulation S or as otherwise
         permitted in Section 7(a); accordingly, neither such Initial Purchaser,
         its Affiliates nor any persons acting on its or their behalf have
         engaged or will engage in any directed selling efforts (within the
         meaning of Regulation S) with respect to the Securities, and any such
         Initial Purchaser, its Affiliates and any such persons have complied
         and will comply with the offering restrictions requirement of
         Regulation S;

                  (v) such Initial Purchaser has (A) not offered or sold and,
         prior to the date six months after the Closing Date, will not offer or
         sell any Securities to persons in the United Kingdom except to persons
         whose ordinary activities involve them in acquiring, holding, managing
         or disposing of investments (as principal or agent) for the purposes of
         their businesses or otherwise in circumstances which have not resulted
         and will not result in an offer to the public in the United Kingdom
         within the meaning of the Public Offers of Securities Regulations 1995;
         (B) complied and will comply with all applicable provisions of the
         Financial Services Act 1986 with respect to anything done by it in
         relation to the Securities in, from or otherwise involving the United
         Kingdom, and (C) only issued or passed on and will only issue or pass
         on in the United Kingdom any document received by it in connection with
         the issue of the Securities to a person who is of a kind described in
         Article 11(3) of the Financial Services Act 1986 (Investment
         Advertisements) (Exemptions) Order 1996 or is a person to whom such
         document may otherwise lawfully be issued or passed on;

                  (vi) such Initial Purchaser understands that the Securities
         have not been and will not be registered under the Securities and
         Exchange Law of Japan, and represents that it has not offered or sold,
         and agrees not to offer or sell, directly or indirectly, any Securities
         in Japan or for the account of any resident thereof except pursuant to
         any exemption from the registration requirements of the Securities and
         Exchange Law of Japan and otherwise in compliance with applicable
         provisions of Japanese law;

                  (vii) such Initial Purchaser understands that the Securities
         have not been and will not be qualified for sale under the securities
         laws of any province or territory of Canada, and represents that it has
         not offered or sold, and agrees not to offer or sell, directly or
         indirectly, any Securities in Canada or to or for the account of any
         resident of Canada in contravention of the securities laws of any
         province or territory thereof; and

                  (viii) such Initial Purchaser agrees that, at or prior to
         confirmation of sales of the Securities, it will have sent to each
         distributor, dealer or person receiving a selling concession, fee or
         other remuneration that purchases Securities from it during the
         restricted period a confirmation or notice to substantially the
         following effect:

                  "The Securities covered hereby have not been registered under
         the U.S. Securities Act of 1933 (the "Securities Act") and may not be
         offered and sold within the United States or to, or for the account or
         benefit of, U.S. persons (i) as part of their distribution at any time
         or (ii) otherwise until 40 days after the later



                                       12
<PAGE>   13

         of the commencement of the offering and the closing date, except in
         either case in accordance with Regulation S (or Rule 144A if available)
         under the Securities Act. Terms used above have the meaning given to
         them by Regulation S."

                  Terms used in this Section 7(b) have the meanings given to
them by Regulation S.

                  8. Indemnity and Contribution. (a) The Company agrees to
indemnify and hold harmless each Initial Purchaser and each person, who controls
any Initial Purchaser within the meaning of either Section 15 of the Securities
Act or Section 20 of the Exchange Act against any and all losses, claims,
damages or liabilities, joint or several (including amounts paid in settlement
of any litigation if such settlement is effected with the written consent of the
Company), to which they or any of them may become subject under the Act, the
Exchange Act or other Federal or state statutory law or regulation, at common
law or otherwise, insofar as such losses, claims, damages or liabilities (or
actions in respect thereof) arise out of or are based upon any untrue statement
or alleged untrue statement of a material fact contained in either Memorandum or
in any amendment thereof, or arise out of or are based upon the omission or
alleged omission to state therein a material fact required to be stated therein
or necessary to make the statements therein not misleading, and agrees to
reimburse each such indemnified party for any legal or other expenses reasonably
incurred by them in connection with investigating or defending any such loss,
claim, damage, liability or action; provided, however, that (i) the Company will
not be liable in any such case to the extent that any such loss, claim, damage
or liability arises out of or is based upon any such untrue statement or alleged
untrue statement or omission or alleged omission made therein in reliance upon
and in conformity with written information furnished to the Company by or on
behalf of any Initial Purchaser specifically for use in connection with the
preparation thereof and (ii) such indemnity with respect to any Memorandum shall
not inure to the benefit of any Initial Purchaser (or any person controlling
such Initial Purchaser) from whom the person asserting any such loss, claim,
damage or liability purchased the Securities which are the subject thereof if
such person did not receive a copy of the Final Memorandum (as amended or
supplemented) excluding documents incorporated therein by reference if such
Initial Purchaser was required by law to deliver such Final Memorandum at or
prior to the confirmation of the sale of such Securities to such person and the
untrue statement or omission of a material fact contained in the Preliminary
Memorandum was corrected in the Final Memorandum (as amended or supplemented).
This indemnity agreement will be in addition to any liability which the Company
may otherwise have.

                  (b) Each Initial Purchaser severally, and not jointly, agrees
to indemnify and hold harmless the Company, each of its directors, each of its
officers and each person who controls the Company within the meaning of either
Section 15 of the Securities Act or Section 20 of the Exchange Act to the same
extent as the foregoing indemnity from the Company to each Initial Purchaser,
but only with reference to written information relating to such Initial
Purchaser furnished to the Company by such Initial Purchaser expressly for use
in either Memorandum or any amendments or supplements thereto. This indemnity
agreement will be in addition to any liability which any Initial Purchaser may
otherwise have.



                                       13
<PAGE>   14

                  (c) Promptly after receipt by an indemnified party under this
Section 8 of notice of the commencement of any action, such indemnified party
will, if a claim in respect thereof is to be made against the indemnifying
party, under this Section 8, notify the indemnifying party in writing of the
commencement thereof; but the omission so to notify the indemnifying party will
not relieve it from any liability which it may have to any indemnified party,
otherwise than under this Section 8. In case any such action is brought against
any indemnified party, and it notifies the indemnifying party of the
commencement thereof, the indemnifying party will be entitled to participate
therein, and to the extent that it may elect by written notice delivered to the
indemnified party promptly after receiving the aforesaid notice from such
indemnified party, to assume the defense thereof, with counsel reasonably
satisfactory to such indemnified party; provided, however, that if the
defendants in any such action include both the indemnified party and the
indemnifying party and the indemnified party shall have reasonably concluded
that there may be legal defenses available to it and/or other indemnified
parties which are different from or additional to those available to the
indemnifying party, the indemnified party, or parties shall have the right to
select separate counsel to assert such legal defenses and to otherwise
participate in the defense of such action on behalf of such indemnified party or
parties. Upon receipt of notice from the indemnifying party to such indemnified
party of its election so to assume the defense of such action and approval by
the indemnified party, of counsel, the indemnifying party will not be liable to
such indemnified party under this Section 8 for any legal or other expenses
subsequently incurred by such indemnified party in connection with the defense
thereof unless (i) the indemnified party shall have employed separate counsel in
connection with the assertion of legal defenses in accordance with the proviso
to the next preceding sentence (it being understood, however, that the
indemnifying party shall not be liable for the expenses of more than one
separate counsel, approved by the Representatives in the case of paragraph (a)
of this Section 8, representing the indemnified parties under such paragraph (a)
who are parties to such action), (ii) the indemnifying party shall not have
employed counsel satisfactory to the indemnified party to represent the
indemnified party within a reasonable time after notice of commencement of the
action or (iii) the indemnifying party has authorized the employment of counsel
for the indemnified party at the expense of the indemnifying party; and except
that, if clause (i) or (iii) is applicable, such liability shall be only in
respect of the counsel referred to in such clause (i) or (iii).

                  (d) To the extent the indemnification provided for in this
Section 8 is unavailable to an indemnified party under paragraph (a) or (b)
hereof or insufficient in respect of any losses, claims, damages or liabilities
referred to therein, then each indemnifying party, in lieu of indemnifying such
indemnified party, shall contribute to the amount paid or payable by such
indemnified party as a result of such losses, claims, damages or liabilities (i)
in such proportion as is appropriate to reflect the relative benefits received
by the Company on the one hand and the Initial Purchasers on the other hand from
the offering of the Securities or (ii) if the allocation provided by clause (i)
above is not permitted by applicable law, in such proportion as is appropriate
to reflect not only the relative benefits referred to in clause (i) above but
also the relative fault of the Company on the one hand and of the Initial
Purchasers on the other in connection with the statements or omissions that
resulted in such losses, claims, damages or liabilities, as well as any other
relevant equitable considerations. The relative benefits



                                       14
<PAGE>   15

received by the Company on the one hand and the Initial Purchasers on the other
in connection with the offering of the Securities shall be deemed to be in the
same proportion as the total net proceeds from the offering of the Securities
(before deducting expenses) received by the Company bear to the total discounts
and commissions received by the Initial Purchasers in respect thereof. The
relative fault of the Company on the one hand and of the Initial Purchasers on
the other shall be determined by reference to, among other things, whether the
untrue or alleged untrue statement of a material fact or the omission or alleged
omission to state a material fact relates to information supplied by the Company
or by the Initial Purchasers and the parties' relative intent, knowledge, access
to information and opportunity to correct or prevent such statement or omission.

                  (e) The Company and the Initial Purchasers agree that it would
not be just and equitable if contribution pursuant to this Section 8 were
determined by pro rata allocation or by any other method of allocation that does
not take account of the equitable considerations referred to in Section 8(d).
The amount paid or payable by an indemnified party as a result of the losses,
claims, damages and liabilities referred to in Section 8(d) shall be deemed to
include, subject to the limitations set forth above, any legal or other expenses
reasonably incurred by such indemnified party in connection with investigating
or defending any such action or claim. Notwithstanding the provisions of this
Section 8, no Initial Purchaser shall be required to contribute any amount in
excess of the amount by which the total price at which the Securities resold by
it in the initial placement of such Securities were offered to investors exceeds
the amount of any damages that such Initial Purchaser has otherwise been
required to pay by reason of such untrue or alleged untrue statement or omission
or alleged omission. No person guilty of fraudulent misrepresentation (within
the meaning of Section 11(f) of the Securities Act) shall be entitled to
contribution from any person who was not guilty of such fraudulent
misrepresentation. The Initial Purchasers' obligations to contribute pursuant to
this Section 8 are several, in proportion to the respective principal amounts of
Securities purchased by each of such Initial Purchasers, and not joint.

                  9. Termination. An Initial Purchaser may terminate this
Agreement, immediately upon notice to the Company, at any time prior to the
Closing Date (a) if there has been, since the date of this Agreement or since
the respective dates as of which information is given in the Final Memorandum,
any change, or any development involving a prospective change, in or affecting
the business or properties of the Company and its subsidiaries, shall have
occurred the effect of which is, in the judgment of Morgan Stanley & Co.
Incorporated, so material and adverse to the Company and its subsidiaries taken
as a whole as to make it impractical or inadvisable to proceed with the delivery
of the Securities or (b) if there shall have occurred any material adverse
change in the financial markets in the United States or any outbreak or
escalation of hostilities or other national or international calamity or crisis,
the effect of which shall be such as to make it, in the judgment of Morgan
Stanley & Co. Incorporated, impracticable to market the Securities or enforce
contracts for the sale of the Securities, or (c) if trading in any securities of
the Company shall have been suspended by the Commission or a national securities
exchange, or if trading generally on either the American Stock Exchange or the
New York Stock Exchange shall have been suspended, or minimum or maximum prices
for trading shall have been fixed, or maximum ranges for prices for securities
shall have been required, by either of said exchanges or by order of the
Commission or any other



                                       15
<PAGE>   16

governmental authority, or if a banking moratorium shall have been declared by
either Federal or New York authorities or if a banking moratorium shall have
been declared by the relevant authorities in the country or countries of origin
of any foreign currency or currencies in which the Securities are denominated or
payable, or (d) if the rating assigned by any nationally recognized securities
rating agency to any debt securities of the Company as of the date of this
Agreement shall have been lowered since that date or if any such rating agency
shall have publicly announced that it has placed any debt securities of the
Company on what is commonly termed a "watch list" for possible downgrading, or
(e) if there shall have come to the attention of such Initial Purchaser any
facts that would cause you to believe that the Final Memorandum, at the time it
was required to be delivered to a purchaser of Securities, contained an untrue
statement of a material fact or omitted to state a material fact necessary in
order to make the statements therein, in light of the circumstances existing at
the time of such delivery, not misleading.

                  10. Effectiveness; Defaulting Initial Purchasers. This
Agreement shall become effective upon the execution and delivery hereof by the
parties hereto.

                  If, on the Closing Date, any one or more of the Initial
Purchasers shall fail to purchase and pay for any of the Securities that it or
they have agreed to purchase hereunder on such date, and such failure to
purchase shall constitute a default in the performance of its or their
obligations under this Agreement, the remaining Initial Purchasers shall be
obligated severally to take up and pay for (in the respective proportions which
the amount of Securities set forth opposite their names in Schedule II hereto
bears to the aggregate amount of Securities set forth opposite their names of
all the remaining Initial Purchasers) the Securities which the defaulting
Initial Purchaser or Initial Purchasers agreed but failed to purchase; provided,
however, that in the event that the aggregate amount of Securities which the
defaulting Initial Purchaser or Initial Purchasers agreed but failed to purchase
shall exceed 10% of the aggregate amount of Securities set forth in Schedule II
hereto, the remaining Initial Purchasers shall have the right to purchase all,
but shall not be under any obligation to purchase any, of the Securities, and if
such nondefaulting Underwriters do not purchase all the Securities, this
Agreement will terminate without liability to any nondefaulting Initial
Purchaser or the Company. In the event of a default by any Initial Purchaser as
set forth in this Section 10, the Closing Date shall be postponed for such
period, not exceeding seven days, as the Representatives shall determine in
order that the required changes in the Final Memorandum or in any other
documents or arrangements may be effective. Nothing contained in this Agreement
shall relieve any defaulting Initial Purchaser of its liability, if any, to the
Company and any nondefaulting Initial Purchaser for damages occasioned by its
default hereunder.

                  If the sale of the Securities provided for herein is not
consummated because any condition to the obligations of the Initial Purchasers
set forth in Section 5 hereof is not satisfied because of any refusal, inability
or failure on the part of the Company to perform any agreement herein or comply
with any provision hereof other than by reason of a default by any of the
Initial Purchasers, the Company will reimburse the Initial Purchasers severally
upon demand for all reasonable out-of-pocket expenses (including reasonable fees
and disbursements of counsel) that shall have been incurred by them in
connection with the proposed purchase and sale of the Securities but the



                                       16
<PAGE>   17

Company shall be under no further liability to the Initial Purchasers with
respect to such Securities except as provided in Section 8 hereof.

                  11. Representatives and Indemnities to Survive. The respective
agreements, representations, warranties, indemnities and other statements of the
Company or its officers and of the Initial Purchasers set forth in or made
pursuant to this Agreement will remain in full force and effect, regardless of
any investigation made by or on behalf of any Initial Purchaser or the Company
or any of the officers, directors or controlling persons referred to in Section
8 hereof, and will survive delivery of and payment for the Securities. The
provisions of the third paragraph of Section 10 and the provisions of Section 8
hereof shall survive the termination or cancellation of this Agreement.

                  12. Counterparts. This Agreement may be signed in any number
of counterparts, each of which shall be an original, with the same effect as if
the signatures thereto and hereto were upon the same instrument.

                  13. Applicable Law. This Agreement shall be governed by and
construed in accordance with the laws of the State of New York.

                  14. Headings. The headings of the sections of this Agreement
have been inserted for convenience of reference only and shall not be deemed a
part of this Agreement.

                  15. Notices. All communications hereunder will be in writing
and effective only on receipt, and, if sent to the Initial Purchasers, will be
mailed, delivered or telegraphed and confirmed to the Representatives of the
Initial Purchasers, at the address specified in Schedule II hereto; or, if sent
to the Company, will be mailed, delivered or telegraphed and confirmed to it,
care of 1900 Richmond Road, Cleveland, Ohio 44124, Attention of the Secretary.

                  16. Successors. This Agreement will inure to the benefit of
and be binding upon the parties hereto and their respective successors and the
officers and directors and controlling persons referred to in Section 8 hereof,
and no other person will have any right or obligation hereunder.


                                       17
<PAGE>   18


                  17. Business Day. For purposes of this Agreement, "business
day" means any day on which the New York Stock Exchange is open for trading.

                  If the foregoing is in accordance with your understanding of
our agreement, please sign and return to us the enclosed duplicate hereof,
whereupon this letter and your acceptance shall represent a binding agreement
between the Company and each of the Initial Purchasers.

                                Very truly yours,

                                TRW INC.


                                By: /s/ Carl G. Miller
                                    Name:    Carl G. Miller
                                    Title:   Executive Vice President
                                             and Chief Financial Officer



                                       18
<PAGE>   19

Accepted as of the date hereof

Morgan Stanley & Co. Incorporated
J.P. Morgan Securities Inc.
Salomon Smith Barney Inc.

Acting severally on behalf of themselves and
       the several Initial Purchasers named in
       Schedule II hereto.

By:    Morgan Stanley & Co. Incorporated       By:  J.P. Morgan Securities Inc.


By:      /s/ Michael Fusco                     By:      /s/ Maria Sramek
    -------------------------------------         ------------------------------
       Name:    Michael Fusco                        Name:   Maria Sramek
       Title:   Vice President                       Title:  Vice President


By:    Salomon Smith Barney Inc.


By:      /s/ Martha D. Bailey
     ------------------------------------
       Name:    Martha D. Bailey
       Title:   Vice President




                                       19
<PAGE>   20

                                                                      SCHEDULE I


Description of the Securities:

Title and Purchase Price of 6 1/2% Notes Due 2002:

Title:                                      61/2% Notes Due 2002

Principal amount:                           $400,000,000

Interest rate:                              6 1/2%

Interest payment dates:                     June 1 and December 1

Date of maturity:                           June 1, 2002

Purchase price (include
  accrued interest or
  amortization, if any):                    99.616%

Initial offering price:                     99.866%


Title and Purchase Price of 6 5/8% Notes Due 2004:

Title:                                      6 5/8% Notes Due 2004

Principal amount:                           $700,000,000

Interest rate:                              6 5/8 %

Interest payment dates:                     June 1 and December 1

Date of maturity:                           June 1, 2004

Purchase price (include
  accrued interest or
  amortization, if any):                    99.002%

Initial offering price:                     99.352%



<PAGE>   21


Title and Purchase Price of 7 1/8% Notes Due 2009:

Title:                                      7 1/8% Notes Due 2009

Principal amount:                           $750,000,000

Interest rate:                              7 1/8%

Interest payment dates:                     June 1 and December 1

Date of maturity:                           June 1, 2009

Purchase price (include
  accrued interest or
  amortization, if any):                    98.602%

Initial offering price:                     99.052%


Title and Purchase Price of 7 3/4% Debentures Due 2029:

Title:                                      7 3/4% Debentures Due 2029

Principal amount:                           $550,000,000

Interest rate:                              7 3/4%

Interest payment dates:                     June 1 and December 1

Date of maturity:                           June 1, 2029

Purchase price (include
  accrued interest or
  amortization, if any):                    98.206%

Initial offering price:                     99.081%

Closing Date, Time and Location:            June 2, 1999, at 9:00 a.m. at the
                                            offices of Cravath, Swaine & Moore,
                                            Worldwide Plaza, 825 Eighth Avenue,
                                            New York, New York 10019


<PAGE>   22


                                                                     SCHEDULE II

$400,000,000 of 6 1/2% Notes Due 2002


<TABLE>
<CAPTION>
                        INITIAL PURCHASERS                                        PRINCIPAL AMOUNT OF 2002
                                                                                     NOTES TO BE PURCHASED

<S>                                                                                      <C>
Morgan Stanley & Co. Incorporated..............................                               $108,000,000

J.P. Morgan Securities Inc.....................................                                108,000,000

Salomon Smith Barney Inc.......................................                                108,000,000

Banc of America Securities LLC.................................                                 13,000,000

Barclays Bank PLC..............................................                                 13,000,000

Chase Securities Inc...........................................                                 13,000,000

Goldman, Sachs & Co............................................                                 13,000,000

Banc One Capital Markets, Inc..................................                                  4,000,000

Blaylock & Partners, L.P.......................................                                  4,000,000

Deutsche Bank Securities Inc...................................                                  4,000,000

Dresdner Bank AG (London Branch)...............................                                  4,000,000

McDonald Investments, Inc. (A KeyCorp Company).................                                  4,000,000

RBC Dominion Securities Corporation............................                                  4,000,000

       Total:..................................................                               $400,000,000
                                                                                              ============
</TABLE>



<PAGE>   23




$700,000,000 of 6 5/8% Notes Due 2004

<TABLE>
<CAPTION>
                        INITIAL PURCHASERS                                        PRINCIPAL AMOUNT OF 2004
                                                                                     NOTES TO BE PURCHASED

<S>                                                                                <C>
Morgan Stanley & Co. Incorporated..............................                               $189,000,000

J.P. Morgan Securities Inc.....................................                                189,000,000

Salomon Smith Barney Inc.......................................                                189,000,000

Banc of America Securities LLC.................................                                 22,750,000

Barclays Bank PLC..............................................                                 22,750,000

Chase Securities Inc...........................................                                 22,750,000

Goldman, Sachs & Co............................................                                 22,750,000

Banc One Capital Markets, Inc..................................                                  7,000,000

Blaylock & Partners, L.P.......................................                                  7,000,000

Deutsche Bank Securities Inc...................................                                  7,000,000

Dresdner Bank AG (London Branch)...............................                                  7,000,000

McDonald Investments, Inc. (A KeyCorp Company).................                                  7,000,000

RBC Dominion Securities Corporation............................                                  7,000,000

       Total:                                                                                 $700,000,000
                                                                                              ============
</TABLE>





<PAGE>   24



$750,000,000 of 7 1/8% Notes Due 2009

<TABLE>
<CAPTION>
                        INITIAL PURCHASERS                                        PRINCIPAL AMOUNT OF 2009
                                                                                     NOTES TO BE PURCHASED

<S>                                                                                  <C>
Morgan Stanley & Co. Incorporated.................................                            $202,500,000

J.P. Morgan Securities Inc........................................                             202,500,000

Salomon Smith Barney Inc..........................................                             202,500,000

Banc of America Securities LLC....................................                              24,375,000

Barclays Bank PLC.................................................                              24,375,000

Chase Securities Inc..............................................                              24,375,000

Goldman, Sachs & Co...............................................                              24,375,000

Banc One Capital Markets, Inc.....................................                               7,500,000

Blaylock & Partners, L.P..........................................                               7,500,000

Deutsche Bank Securities Inc......................................                               7,500,000

Dresdner Bank AG (London Branch)..................................                               7,500,000

McDonald Investments, Inc. (A KeyCorp Company)....................                               7,500,000

RBC Dominion Securities Corporation...............................                               7,500,000

               Total:.............................................                            $750,000,000
                                                                                              ============
</TABLE>


<PAGE>   25



$550,000,000 of 7 3/4% Debentures Due 2029

<TABLE>
<CAPTION>
                        INITIAL PURCHASERS                                        PRINCIPAL AMOUNT OF 2029
                                                                                     NOTES TO BE PURCHASED

<S>                                                                                           <C>
Morgan Stanley & Co. Incorporated.................................                            $148,500,000

J.P. Morgan Securities Inc........................................                             148,500,000

Salomon Smith Barney Inc..........................................                             148,500,000

Banc of America Securities LLC....................................                              17,875,000

Barclays Bank PLC.................................................                              17,875,000

Chase Securities Inc..............................................                              17,875,000

Goldman, Sachs & Co...............................................                              17,875,000

Banc One Capital Markets, Inc.....................................                               5,500,000

Blaylock & Partners, L.P..........................................                               5,500,000

Deutsche Bank Securities Inc......................................                               5,500,000

Dresdner Bank AG (London Branch)..................................                               5,500,000

McDonald Investments, Inc. (A KeyCorp Company)....................                               5,500,000

RBC Dominion Securities Corporation...............................                               5,500,000

         Total:...................................................                            $550,000,000
                                                                                              ============
</TABLE>



<PAGE>   26


                                                                       EXHIBIT A



                     FORM OF OPINION OF WILLIAM B. LAWRENCE

Gentlemen and Ladies:

This opinion is addressed to you with respect to $400,000,000 in aggregate
principal amount of 6 1/2% Notes Due 2002, $700,000,000 aggregate principal
amount of 6 5/8% Notes Due 2004, $750,000,000 aggregate principal amount of 7
1/8% Notes Due 2009, and $550,000,000 aggregate principal amount of 7 3/4%
Debentures Due 2029 (collectively, the "Offered Securities") of TRW Inc., an
Ohio corporation (the "Company"), to be issued under an Indenture dated as of
May 1, 1986, supplemented by the First Supplemental Indenture dated August 24,
1989, the Second Supplemental Indenture dated as of June 2, 1999, the Third
Supplemental Indenture dated as of June 2, 1999, the Fourth Supplemental
Indenture dated as of June 2, 1999, and the Fifth Supplemental Indenture dated
as of June 2, 1999 (as supplemented, the "Indenture"), between the Company and
The Chase Manhattan Bank as successor trustee ("Trustee") to Mellon Bank, N.A.,
pursuant to Section 5(b) of the Purchase Agreement dated May 26, 1999 (the
"Purchase Agreement"), entered into among the Company and each of you as
representatives (the "Representatives"). Capitalized terms used but not defined
in this letter are used as defined in the Purchase Agreement.

I am General Counsel of the Company and have acted in such capacity in
connection with the proposed issue and sale by the Company of the Offered
Securities. With respect thereto, I have examined or caused to be examined by
members of the TRW Law Department the following: (i) the Amended Articles of
Incorporation of the Company; (ii) the Regulations of the Company; (iii) the
corporate proceedings of the Company relating to the Offered Securities, the
Final Offering Memorandum (as defined below), and the execution and delivery of
the Purchase Agreement, the Registration Rights Agreement and the Indenture;
(iv) the Company's Annual Report on Form 10-K for the year ended December 31,
1998, the Company's Quarterly Reports on Form 10-Q for the quarter ended March
31, 1999, the Company's Current Reports on Form 8-K dated as of January 28,
1999, February 5, 1999, March 26, 1999 (as amended May 17, 1999) (the
"Incorporated Documents"), all of which documents have been filed with the
Securities and Exchange Commission (the "Commission") pursuant to the Securities
Exchange Act of 1934, as amended (the "Exchange Act"), and are incorporated by
reference in the Final Offering Memorandum; (v) the Offering Memorandum dated
May 26, 1999 (the "Final Offering Memorandum"); (vi) the Purchase Agreement;
(vii) the Indenture; (viii) the Registration Rights Agreement and (ix) the Form
of the Offered Securities.



<PAGE>   27

I have also made or caused to be made such other examinations as I have deemed
necessary to enable me to give the opinions herein expressed. However, as to
each of the opinions set forth below which is limited to my knowledge, you
should be aware that I have neither made nor caused to be made any independent
review for purposes of rendering this opinion, although in the regular course of
advising TRW I have reviewed or caused to be reviewed various documents, records
and matters of law. As to matters relating to that portion of the Company that
constituted LucasVarity plc ("LucasVarity") prior to its purchase by the
Company, I have relied on the opinion of Russell Kelley, General Counsel of
LucasVarity Ltd. As to matters relating to Lucas Limited and governed by English
law, I have relied on the opinion of Allen & Overy.

Based upon the foregoing, I am of the opinion that:

1. The Company is a corporation duly organized, validly existing and in good
standing under the laws of the State of Ohio, with full corporate power and
authority to own its properties and conduct the business now being conducted by
it as described in the Final Offering Memorandum, and is duly qualified to do
business as a foreign corporation in each jurisdiction which requires such
qualification wherein it owns or leases material properties or conducts material
business, except where the failure to so qualify would not have a material
adverse effect on the financial condition or the earnings, business affairs or
business prospects of the Company and its subsidiaries considered as one
enterprise; and the Company is in good standing in the State of California and
the Commonwealth of Virginia;

2. Lucas Limited, a private limited company organized and existing under the
laws of England and Wales ("Lucas Limited"), is duly incorporated, validly
existing and in good standing as a private company with limited liability under
the laws of England. The registers of charges of Lucas Limited's immediate
holding company, Lucas Investment Finance Limited, and of Joseph Lucas Limited,
as at June 2, 1999, do not disclose any charges over the shares in Lucas Limited
held by them. Each of the certificate of incorporation and Memorandum and
Articles of Association of Lucas Limited do not prohibit Lucas Limited from
engaging in the business of producing and selling automotive and aerospace
products;

3. Kelsey-Hayes Company, a Delaware corporation ("Kelsey-Hayes"), has been duly
incorporated, is validly existing as a corporation in good standing under the
laws of the jurisdiction of its incorporation or organization has the corporate
power and authority to own its property and to conduct its business as described
in the Final Memorandum and is duly qualified to transact business and is in
good standing in each jurisdiction in which the conduct of its business or its
ownership or leasing of property requires such qualification, except to the
extent that the failure to be so qualified or be in good standing would not have
a material adverse effect on the financial condition, or the earnings,



<PAGE>   28

business affairs or business prospects of the Company and its subsidiaries,
taken as a whole; all of the issued shares of capital stock of Kelsey-Hayes have
been duly and validly authorized and issued, are fully paid and non-assessable,
and are owned directly or indirectly, free and clear of all liens, encumbrances,
equities or claims;

4. Each of the Indenture and the Registration Rights Agreement has been duly
authorized, executed and delivered by or on behalf of the Company, and
constitutes a legal, valid and binding instrument enforceable against the
Company in accordance with its terms except (i) as rights to indemnification and
contribution under the Registration Rights Agreement may be limited under
applicable law and (ii) as the enforcement of remedies may be (A) limited by
applicable bankruptcy, reorganization, insolvency, moratorium or other laws or
proceedings affecting the enforcement of creditors' rights generally from time
to time in effect or (B) subject to the effect of general principles of equity,
whether applied by a court of law or equity; and the Offered Securities have
been duly authorized and, when executed and authenticated in accordance with the
provisions of the Indenture and delivered to and paid for by the Initial
Purchasers pursuant to the Purchase Agreement, will constitute legal, valid and
binding obligations of the Company entitled to the benefits of the Indenture,
the Registration Rights Agreement and the Purchase Agreement except as the
enforcement of remedies may be (i) limited by applicable bankruptcy,
reorganization, insolvency, moratorium or other laws or proceedings affecting
the enforcement of creditors' rights generally from time to time in effect or
(ii) subject to the effect of general principles of equity, whether applied by a
court of law or equity;

5. To my knowledge, there is no pending or threatened action, suit or proceeding
before any court or governmental agency, authority or body or any arbitrator
involving the Company or any of its subsidiaries, of a character that would be
required to be disclosed in a registration statement filed under the Securities
Act of 1933, as amended (the "Act"), which is not adequately disclosed in the
Final Memorandum, and there is no franchise, contract or other document of a
character that would be required to be described in a registration statement or
prospectus filed under the Act, or to be filed as an exhibit, which is not
described or filed as required; and the statements included or incorporated in
the Final Memorandum describing any legal proceedings or material contracts or
agreements relating to the Company fairly summarize such matters;

6. I have no reason to believe that the Final Memorandum, or any amendment
thereof, at the date of this letter contained any untrue statement of a material
fact or omitted to state any material fact required to be stated therein or
necessary to make the statements therein not misleading or that the Final
Memorandum, as amended or supplemented, at the date of this letter, includes any
untrue statement of a material fact or omits to state a material fact necessary
to make the statements therein, in the light of the circumstances under which
they were made, not misleading; PROVIDED, HOWEVER, that I express no opinion as
to


<PAGE>   29

the information contained in or omitted from the Final Memorandum or any
amendment thereof or supplement thereto in reliance upon and in conformity with
written information furnished to the Company by or on behalf of any Initial
Purchaser specifically for use in connection with the preparation of the Final
Memorandum or any amendment thereof or supplement thereto;

7. The Purchase Agreement has been duly authorized, executed and delivered by
the Company;

8. No consent, approval, authorization or order of any court or governmental
agency or body is required for the consummation of the transactions contemplated
herein except such as have been obtained under the Act and such as may be
required under the blue sky laws of any jurisdiction in connection with the
purchase and distribution of the Securities by the Initial Purchasers;

9. Neither the issue and sale of the Securities, nor the consummation of any
other of the transactions contemplated by the Purchase Agreement nor the
fulfillment of the terms of the Purchase Agreement, the Indenture, the
Registration Rights Agreement and the Securities will conflict with, result in a
breach of, or constitute a default under, the Amended Articles of Incorporation
or Regulations of the Company or the terms of any indenture or other agreement
or instrument known to me and to which the Company is a party or bound, or any
order or regulation known to me to be applicable to the Company of any court,
regulatory body, administrative agency, governmental body or arbitrator having
jurisdiction over the Company; and

10. Based upon the representations, warranties and agreements of the Company in
Sections 1(m), 1(n), 1(o), 6(f), 6(g) and 6(j) of the Purchase Agreement and of
the Initial Purchasers in Section 7 of the Purchase Agreement, and assuming (i)
the accuracy of the representations and warranties of each of the purchasers to
whom the Initial Purchasers initially resell the Securities, (ii) compliance by
the Initial Purchasers with the offering and transfer procedures and
restrictions described in the Offering Memorandum and (iii) receipt by the
purchasers to whom the Initial Purchasers initially resell the Securities of a
copy of the Offering Memorandum prior to such sale, it is not necessary in
connection with the offer, sale and delivery of the Securities to the Initial
Purchasers under the Purchase Agreement or in connection with the initial resale
of such Securities by the Initial Purchasers in accordance with Section 7 of the
Purchase Agreement to register the Securities under the Securities Act of 1933,
or to qualify the Indenture under the Trust Indenture Act of 1939, it being
understood that no opinion is expressed as to any subsequent resale of any
Security.



<PAGE>   30

I am a member of the bar of the State of Ohio and do not purport to be an expert
on, generally familiar with or qualified to express legal conclusions based on
laws other than the laws of the State of Ohio and the United States of America.

This opinion is being delivered to the Initial Purchasers solely for their
benefit as representatives under the Purchase Agreement and Initial Purchasers
and may be relied upon only by you for such purpose.

Very truly yours,


William B. Lawrence
General Counsel


<PAGE>   31




                                    EXHIBIT B

                   FORM OF OPINION OF CRAVATH, SWAINE & MOORE

                                    TRW Inc.
                       $400,000,000 6 1/2% Notes Due 2002
                       $700,000,000 6 5/8% Notes Due 2004
                       $750,000,000 7 1/8% Notes Due 2009
                     $550,000,000 7 3/4% Debentures Due 2029



Ladies and Gentlemen:

                  We have acted as your counsel in connection with the purchase
by you, pursuant to the Purchase Agreement dated May 26, 1999 (the "Purchase
Agreement"), among you and TRW Inc., an Ohio corporation (the "Company"), of
$400,000,000 principal amount of the Company's 6 1/2% Notes Due 2002,
$700,000,000 principal amount of the Company's 6 5/8% Notes Due 2004,
$750,000,000 principal amount of the Company's 7 1/8% Notes Due 2009 and
$550,000,000 principal amount of the Company's 7 3/4% Debentures Due 2029
(collectively, the "Securities") to be issued under the Indenture dated as of
May 1, 1986, as supplemented and amended by the First Supplemental Indenture
dated as of August 24, 1989, the Second Supplemental Indenture dated as of June
2, 1999, the Third Supplemental Indenture dated as of June 2, 1999, the Fourth
Supplemental Indenture dated as of June 2, 1999, and the Fifth Supplemental
Indenture dated June 2, 1999 (the "Indenture"), between the Company and The
Chase Manhattan Bank, as Trustee. Capitalized terms used and not otherwise
defined herein have the meanings ascribed thereto in the Purchase Agreement.

                  In that connection, we have examined originals, or copies
certified or otherwise identified to our satisfaction, of such documents,
corporate records and other instruments as we have deemed necessary or
appropriate for the purposes of this opinion, including: (a) resolutions adopted
by the Board of Directors of the Company on February 10, 1999; (b) the Offering
Memorandum dated May 26, 1999 (the "Offering Memorandum"); (c) the Purchase
Agreement; (d) the Registration Rights Agreement; (e) the Indenture; and (f) the
form of the Securities.

                  Based on the foregoing, we are of opinion as follows:



<PAGE>   32

                  1. Assuming that the Indenture has been duly authorized,
executed and delivered by the Company, the Indenture constitutes a legal, valid
and binding obligation of the Company enforceable in accordance with its terms
(subject to applicable bankruptcy, insolvency, fraudulent transfer,
reorganization, moratorium and other similar laws affecting creditors' rights
generally from time to time in effect and to general principles of equity,
including concepts of materiality, reasonableness, good faith and fair dealing,
regardless of whether considered in a proceeding in equity or at law).

                  2. The Securities conform in all material respects to the
description thereof contained in the Offering Memorandum. Assuming that the
Securities have been duly authorized, when executed and authenticated in
accordance with the provisions of the Indenture and delivered to and paid for by
the Initial Purchasers pursuant to the Purchase Agreement, will constitute
legal, valid and binding obligations of the Company entitled to the benefits of
the Indenture and enforceable against the Company in accordance with their terms
(subject to applicable bankruptcy, insolvency, fraudulent transfer,
reorganization, moratorium and other similar laws affecting creditors' rights
generally from time to time in effect and to general principles of equity,
including concepts of materiality, reasonableness, good faith and fair dealing,
regardless of whether considered in a proceeding in equity or at law).

                  3. Assuming (i) the accuracy of, and compliance with, the
representations, warranties and covenants of the Company in the Purchase
Agreement, (ii) the accuracy of, and compliance with, the representations,
warranties and covenants of the Initial Purchasers in the Purchase Agreement,
(iii) the accuracy of the representations and warranties of each of the
purchasers to whom the Initial Purchasers initially resell the Securities, (iv)
compliance by the Initial Purchasers with the offering and transfer procedures
and restrictions described in the Offering Memorandum and (v) receipt by the
purchasers to whom the Initial Purchasers initially resell the Securities of a
copy of the Offering Memorandum prior to such sale, it is not necessary in
connection with the offer, sale and delivery of the Securities or in connection
with the initial resale of such Securities in the manner contemplated by the
Purchase Agreement and the Offering Memorandum to register the Securities under
the Securities Act of 1933, as amended, and the Indenture does not require
qualification under the Trust Indenture Act of 1939, as amended, it being
understood that no opinion is expressed as to any subsequent resale of any
Securities.

                  Although we have not performed an independent verification of
the substance of counsel's opinion and take no responsibility therefor, the
opinion dated the date hereof of William B. Lawrence, General Counsel for the
Company, delivered to you pursuant to Section 5(b) of the Purchase Agreement, is
substantially responsive to the requirements of the Purchase Agreement. This
letter is delivered to you pursuant to Section 5(c) of the Purchase Agreement.



<PAGE>   33

                  We are admitted to practice in the State of New York, and we
express no opinion as to matters governed by any laws other than the laws of the
State of New York, the General Corporation Law of the State of Delaware and the
Federal laws of the United States of America. In particular, we do not purport
to pass on any matter governed by the laws of the State of Ohio. In rendering
this opinion, we have assumed without independent investigation, the correctness
of, and take no responsibility for, the opinion dated June 2, 1999, of William
B. Lawrence, General Counsel for the Company, a copy of which has been delivered
to you pursuant to Section 5(b) of the Purchase Agreement, as to all matters of
law covered therein relating to the laws of the State of Ohio.


<PAGE>   34



                  We are furnishing this opinion to you solely for your benefit.
This opinion may not be relied upon by any other person or for any other purpose
or used, circulated, quoted or otherwise referred to for any other purpose.

                                             Very truly yours,



Morgan Stanley & Co. Incorporated
J.P. Morgan Securities Inc.
Salomon Smith Barney Inc.
Banc of America Securities LLC
Barclays Bank PLC
Chase Securities Inc.
Goldman, Sachs & Co.
Banc One Capital Markets, Inc.
Blaylock & Partners, L.P.
Deutsche Bank Securities Inc.
Dresdner Bank AG (London Branch)
McDonald Investments, Inc. (A KeyCorp Company)
RBC Dominion Securities Corporation


In care of Morgan Stanley & Co. Incorporated
                         1585 Broadway
                              New York, NY 10036

                    J.P. Morgan Securities Inc.
                         60 Wall Street
                              New York, NY 10260

                    Salomon Smith Barney Inc.
                         Seven World Trade Center
                              New York, NY 10048