<PAGE>   1
                                    FORM 10-Q


                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                   (Mark One)

          [ X ] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                  For the quarterly period ended March 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                      1-2384
                               -----------------------------------------

                                 TRW Inc. 
             -----------------------------------------------------
             (Exact name of registrant as specified in its charter)

                    Ohio                                     34-0575430
      -------------------------------                    ------------------
      (State or other jurisdiction of                     (I.R.S.Employer
        incorporation or organization)                   Identification No.)



                    1900 Richmond Road, Cleveland, Ohio 44124
                    -----------------------------------------
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (216) 291-7000
               --------------------------------------------------
              (Registrant's telephone number, including area code)

        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
                                         ------     ------

              As of April 3, 1998, there were 122,650,314 shares of
                TRW Common Stock, $0.625 par value, outstanding.



<PAGE>   2


PART I.  FINANCIAL INFORMATION

Item 1.  Financial Statements
         --------------------

<TABLE>
<CAPTION>

Statements of Earnings (unaudited)
TRW Inc. and subsidiaries
----------------------------------------------------------------------------------------------------------------------
                                                                                                   Quarter ended
                                                                                                     March 31
In millions except per share data                                                             1998              1997
---------------------------------------------------------------------------------------------------------------------

<S>                                                                                          <C>            <C>    
Sales                                                                                        $ 3,095        $ 2,660
Cost of sales                                                                                  2,575          2,178
-------------------------------------------------------------------------------------------------------------------
Gross profit                                                                                     520            482

Administrative and selling expenses                                                              199            159
Research and development expenses                                                                121            106
Interest expense                                                                                  38             20
Other (income) expense-net                                                                       (42)             2
-------------------------------------------------------------------------------------------------------------------
Earnings before income taxes                                                                     204            195
Income taxes                                                                                      75             76
-------------------------------------------------------------------------------------------------------------------
Net earnings                                                                                 $   129        $   119
-------------------------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------------

PER SHARE OF COMMON STOCK
   Diluted earnings per share                                                                $  1.03        $   .92
   Basic earnings per share                                                                  $  1.05        $   .95
   Dividends declared                                                                        $   .00        $   .00
-------------------------------------------------------------------------------------------------------------------

-------------------------------------------------------------------------------------------------------------------
Shares used in computing per share amounts
     Diluted                                                                                   126.2          129.4
     Basic                                                                                     122.6          125.2
-------------------------------------------------------------------------------------------------------------------
</TABLE>



<PAGE>   3
<TABLE>
<CAPTION>



Balance Sheets (unaudited)
TRW Inc. and subsidiaries
-------------------------------------------------------------------------------------------------------------------

                                                                                     March 31       December 31
In millions                                                                            1998             1997
-------------------------------------------------------------------------------------------------------------------

Assets
Current assets
<S>                                                                                    <C>            <C>    
     Cash and cash equivalents                                                         $    92        $    70
     Accounts receivable                                                                 1,772          1,617
     Inventories                                                                           589            573
     Prepaid expenses                                                                       91             79
     Deferred income taxes                                                                 158             96
-------------------------------------------------------------------------------------------------------------
Total current assets                                                                     2,702          2,435

Property, plant and equipment-on the basis of cost                                       6,223          6,074
     Less accumulated depreciation and amortization                                      3,617          3,453
-------------------------------------------------------------------------------------------------------------
Total property, plant and equipment-net                                                  2,606          2,621

Intangible assets
     Intangibles arising from acquisitions                                                 750            673
     Other                                                                                 308            232
-------------------------------------------------------------------------------------------------------------
                                                                                         1,058            905
     Less accumulated amortization                                                         104             94
-------------------------------------------------------------------------------------------------------------
Total intangible assets-net                                                                954            811
Investments in affiliated companies                                                        197            139
Other assets                                                                               440            404
-------------------------------------------------------------------------------------------------------------
                                                                                       $ 6,899        $ 6,410
-------------------------------------------------------------------------------------------------------------

Liabilities and shareholders' investment
Current liabilities
     Short-term debt                                                                   $   694        $   411
     Accounts payable                                                                      840            859
     Current portion of long-term debt                                                      25            128
     Other current liabilities                                                           1,225          1,321
-------------------------------------------------------------------------------------------------------------
Total current liabilities                                                                2,784          2,719

Long-term liabilities                                                                      826            788
Long-term debt                                                                           1,423          1,117
Deferred income taxes                                                                       52             57

Minority interests in subsidiaries                                                          87            105

Capital stock                                                                               77             79
Other capital                                                                              454            450
Retained earnings                                                                        1,844          1,778
Accumulated other comprehensive income                                                    (141)          (120)
Treasury shares-cost in excess of par value                                               (507)          (563)
-------------------------------------------------------------------------------------------------------------
Total shareholders' investment                                                           1,727          1,624
-------------------------------------------------------------------------------------------------------------
                                                                                       $ 6,899        $ 6,410
-------------------------------------------------------------------------------------------------------------

</TABLE>





<PAGE>   4

<TABLE>
<CAPTION>




Statements of Cash Flows (unaudited)
TRW Inc. and subsidiaries
-------------------------------------------------------------------------------------------------------------------
                                                                                              Quarter ended
                                                                                                  March 31
In millions                                                                                   1998          1997
----------------------------------------------------------------------------------------------------------------

Operating activities
<S>                                                                                          <C>           <C>  
Net earnings                                                                                 $ 129         $ 119
Adjustments to reconcile net earnings to net cash
     provided by operating activities:
     Depreciation and amortization                                                             135           127
     Deferred income taxes                                                                     (68)            5
     Other-net                                                                                   5            10
Changes in assets and liabilities, net of effects of businesses acquired:
     Accounts receivable                                                                      (162)         (156)
     Inventories and prepaid expenses                                                          (23)            7
     Accounts payable and other accruals                                                       (29)          (43)
     Other-net                                                                                 (33)          (13)
----------------------------------------------------------------------------------------------------------------
Net cash provided(used in) by operating activities                                             (46)           56
----------------------------------------------------------------------------------------------------------------

Investing activities
Capital expenditures                                                                          (119)          (99)
Acquisitions, net of cash acquired                                                            (228)         (415)
Other-net                                                                                       (8)           16
----------------------------------------------------------------------------------------------------------------
Net cash used in investing activities                                                         (355)         (498)
----------------------------------------------------------------------------------------------------------------

Financing activities
Increase(decrease) in short-term debt                                                          (40)          223
Proceeds from debt in excess of 90 days                                                        620            10
Principal payments on debt in excess of 90 days                                               (110)          (11)
Reacquisition of common stock                                                                  (24)          (77)
Dividends paid                                                                                 (38)          (39)
Other-net                                                                                       14            13
----------------------------------------------------------------------------------------------------------------
Net cash provided by financing activities                                                      422           119
----------------------------------------------------------------------------------------------------------------
Effect of exchange rate changes on cash                                                          1            (4)
----------------------------------------------------------------------------------------------------------------
Increase(decrease) in cash and cash equivalents                                                 22          (327)
Cash and cash equivalents at beginning of quarter                                               70           386
----------------------------------------------------------------------------------------------------------------
Cash and cash equivalents at end of quarter                                                  $  92         $  59
----------------------------------------------------------------------------------------------------------------

</TABLE>



<PAGE>   5

<TABLE>
<CAPTION>



Results by Business Segments (unaudited)
TRW Inc. and subsidiaries
----------------------------------------------------------------------------------------------------------------------
                                                                                                  Quarter ended
                                                                                                    March 31
In millions                                                                                 1998              1997
----------------------------------------------------------------------------------------------------------------------

Sales
<S>                                                                                       <C>             <C>      
Automotive                                                                                $   1,886       $   1,793
Space, Defense & Information Systems                                                          1,209             867
----------------------------------------------------------------------------------------------------------------------
Sales                                                                                     $   3,095       $   2,660
----------------------------------------------------------------------------------------------------------------------



Operating profit
Automotive                                                                                $     147       $     167
Space, Defense & Information Systems                                                            115              77
----------------------------------------------------------------------------------------------------------------------
Operating profit                                                                                262             244
Company Staff and other                                                                         (16)            (24)
Minority interest in earnings of consolidated subsidiaries                                       (5)             (6)
Interest expense                                                                                (38)            (20)
Earnings from affiliates                                                                          1               1
----------------------------------------------------------------------------------------------------------------------
Earnings before income taxes                                                              $     204       $     195
----------------------------------------------------------------------------------------------------------------------
</TABLE>



<PAGE>   6


NOTES TO FINANCIAL STATEMENTS
(unaudited)


Principles of Consolidation
---------------------------

The financial statements include the accounts of the Company and its
subsidiaries except for two insurance subsidiaries. The wholly owned insurance
subsidiaries and the majority of investments in affiliated companies, which are
not significant individually, are accounted for by the equity method.


Comprehensive Income
--------------------

Effective January 1, 1998 the Company adopted Statement of Financial Accounting
Standards No. 130, "Reporting Comprehensive Income." Statement 130
establishes new rules for the reporting and display of comprehensive income and
its components. The adoption of this Statement requires unrealized gains or
losses on the Company's available-for-sale securities, foreign currency
translation and minimum pension liability adjustments be included in other
comprehensive income, which prior to adoption were reported separately in
shareholders' equity. Prior year financial statements have been reclassified to
conform to the requirements of Statement 130.

The components of comprehensive income, net of related tax, for the first
quarter of 1998 and 1997 are as follows:
<TABLE>
<CAPTION>

                                                                                     Quarter ended
(In millions)                                                                          March 31
                                                                        -----------------------------------
                                                                               1998                 1997
                                                                               ----                 ----

<S>                                                                           <C>                  <C>  
Net earnings                                                                  $ 129                $ 119
Unrealized gains on securities                                                    2                    -
Foreign currency translation adjustments                                        (23)                 (63)
                                                                               ----                 ----
Comprehensive income                                                          $ 108                $  56
                                                                               ----                 ----
</TABLE>

The components of accumulated other comprehensive income, net of related tax, at
March 31, 1998 and December 31, 1997 are as follows:
<TABLE>
<CAPTION>

                                                                               March 31           December 31
(In millions)                                                                   1998                  1997
                                                                       -------------------- ---------------------
<S>                                                                          <C>                  <C>
Unrealized gains on securities                                                $  14                $  12
Foreign currency translation adjustments                                       (153)                (130)
Minimum pension liability adjustments                                            (2)                  (2)
                                                                               ----                 ----
Accumulated other comprehensive income                                        $(141)               $(120)
                                                                               ----                 ----
</TABLE>





<PAGE>   7


Inventories
-----------

Inventories consist of the following:
<TABLE>
<CAPTION>

(In millions)                                                                  March 31           December 31
                                                                                   1998               1997
                                                                       ----------------------------------------

<S>                                                                                <C>                   <C> 
Finished products and work in process                                              $326                  $292
Raw materials and supplies                                                          263                   281
                                                                                    ---                   ---
                                                                                   $589                  $573
                                                                                    ---                   ---
</TABLE>


Long-Term Liabilities
---------------------

Long-term liabilities at March 31, 1998, and December 31, 1997, include $660
million and $653 million, respectively, relating to postretirement benefits
other than pensions.


Other (Income)Expense-Net
-------------------------

Other (income)expense-net included the following:
<TABLE>
<CAPTION>

(In millions)                                                                          Quarter ended
                                                                                         March 31
                                                                       ------------------------------------------
                                                                                   1998                 1997
                                                                                   ----                 ----

<S>                                                                                <C>                  <C>  
Other income                                                                       $(66)                $(16)
Other expense                                                                        22                   16
Foreign currency translation                                                          2                    2
                                                                                    ---                  ---
                                                                                   $(42)                $  2
                                                                                    ----                 ---
</TABLE>

First quarter 1998 other income included a $48.5 million benefit from the
settlement of certain patent litigation.


Supplemental Cash Flow Information
----------------------------------
<TABLE>
<CAPTION>

                                                                                     Quarter ended
(In millions)                                                                          March 31
                                                                       ---------------------------------------
                                                                              1998                 1997
                                                                              ----                 ----

<S>                                                                           <C>                 <C>  
Interest paid (net of amount capitalized)                                     $ 30                $  20
Income taxes paid (net of refunds)                                            $ 41                $ (37)

</TABLE>

For purposes of the statements of cash flows, the Company considers all highly
liquid investments purchased with a maturity of three months or less to be cash
equivalents.





<PAGE>   8


Earnings Per Share
------------------

In the fourth quarter of 1997, the Company adopted Statement of Financial
Accounting Standards No. 128, "Earnings per Share." Statement 128 replaced the
calculation of primary and fully diluted earnings per share with basic and
diluted earnings per share. All earnings per share amounts for all periods
presented have been restated to conform to Statement 128 requirements. 
<TABLE>
<CAPTION>

In millions except per share data                                                    Quarter ended
                                                                                       March 31
                                                                        ----------------------------------------
                                                                                  1998                1997
                                                                                  ----                ----
NUMERATOR
<S>                                                                             <C>                 <C>   
  Net earnings                                                                  $129.4              $119.2
  Preferred stock dividends                                                         .2                  .1
                                                                                 -----               -----
  Numerator for basic earnings per
   share--earnings available to common
   shareholders                                                                  129.2               119.1

  Effect of dilutive securities
    Preferred stock dividends                                                       .2                  .1
                                                                                 -----               -----

  Numerator for diluted earnings per share--
   earnings available to common
   shareholders after assumed conversions                                       $129.4              $119.2
                                                                                 -----               -----

DENOMINATOR
  Denominator for basic earnings per
   share--weighted-average common shares                                         122.6               125.2

  Effect of dilutive securities
    Convertible preferred stock                                                     .9                 1.0
    Employee stock options                                                         2.7                 3.2
                                                                                 -----               -----
  Dilutive potential common shares                                                 3.6                 4.2

  Denominator for diluted earnings per
   share--adjusted weighted-average shares and
   assumed conversions                                                           126.2               129.4
                                                                                 -----               -----

Basic earnings per share                                                        $ 1.05              $  .95
                                                                                 -----               -----

Diluted earnings per share                                                      $ 1.03              $  .92
                                                                                 -----               -----

</TABLE>

Contingencies
-------------

During 1997, TRW Vehicle Safety Systems Inc., a wholly owned subsidiary of the
Company, reported to the Arizona Department of Environmental Quality ("ADEQ")
potential violations of the Arizona hazardous waste law at its Queen Creek,
Arizona facility for the possible failure to properly label and dispose of
wastewater that might be classified as hazardous waste. ADEQ is conducting an
investigation into these potential violations and the Company is cooperating
with the investigation. If ADEQ initiates proceedings against the Company with
respect to such matters, the Company could be liable for penalties and fines and
other relief. The Company has been apprised by state and federal officials that
there are ongoing civil and criminal investigations with 

<PAGE>   9

respect to these potential violations. Management is currently evaluating this
matter and is unable to make a meaningful estimate of the amount or range of
possible liability, if any, at this time, although management believes that the
Company would have meritorious defenses.

During 1996, the Company was advised by the Department of Justice ("DOJ") that
it had been named as a defendant in two lawsuits brought by a former employee of
the Company's former Space & Technology Group and originally filed under seal in
1994 and 1995, respectively, in the United States District Court for the Central
District of California under the QUI TAM provisions of the civil False Claims
Act. The Act permits an individual to bring suit in the name of the United
States and share in any recovery. The allegations in the lawsuits relate to the
classification of costs incurred by the Company that were charged to certain of
its federal contracts. Under the law, the government must investigate the
allegations and determine whether it wishes to intervene and take responsibility
for the lawsuits. On February 13, 1998, the DOJ intervened in the litigation. On
February 19, 1998 and March 4, 1998, the former employee filed amended
complaints in the Central District of California that realleged certain of the
claims included in the 1994 and 1995 lawsuits and omitted the remainder. The
amended complaints allege that the United States has incurred substantial
damages and that the Company should be ordered to cease and desist from
violations of the civil False Claims Act and is liable for treble damages,
penalties, costs, including attorneys' fees, and such other relief as deemed
proper by the court. On March 17, 1998, the DOJ filed its complaint against the
Company upon intervention in the 1994 lawsuit, which set forth a limited number
of the allegations in the 1994 lawsuit and other allegations not in the 1994
lawsuit. The DOJ elected not to pursue the other claims in the 1994 lawsuit or
the claims in the 1995 lawsuit. The DOJ's complaint alleges that the Company is
liable for treble damages, penalties, interest, costs and "other proper relief."
On March 18, 1998, the former employee withdrew the first amended complaint in
the 1994 lawsuit at the request of the DOJ. The Company expects to file
responses to the former employee's first amended complaint in the 1995 lawsuit
and the DOJ's complaint during the second quarter of 1998 and intends to defend
itself vigorously. The Company cannot presently predict the outcome of these
lawsuits, although management believes that their ultimate resolution will not
have a material effect on the Company's financial condition or results of
operations.


Interim Statements
------------------

The financial statements are based in part on approximations and are subject to
adjustments that may develop, such as unsettled contract and renegotiation
matters and matters that arise in connection with the annual audit of the
financial statements; however, in the opinion of management, all adjustments
(which consist of normal recurring accruals) necessary for a fair presentation
of the results of operations for the periods presented have been included.
Results of operations for any interim period are not necessarily indicative of
the results to be expected for the full year.



<PAGE>   10


Item 2.     Management's Discussion and Analysis of Financial Condition and 
            --------------------------------------------------------------- 
            Results of Operations
            ---------------------

RESULTS OF OPERATIONS

(In millions except per share data)
<TABLE>
<CAPTION>

                                                                                   First Quarter
                                                               -------------------------------------------------------
                                                                                                          Percent
                                                                   1998                  1997            Inc(Dec)
                                                               ---------------    ----------------    ----------------

<S>                                                              <C>                <C>                   <C>
Sales                                                            $3,095             $2,660                16%
Operating Profit                                                    262                244                 7%
Net Earnings                                                        129                119                 8%
Diluted Earnings Per Share                                         1.03                .92                12%
Effective Tax Rate                                                36.50%             38.75%
</TABLE>

The increase in sales resulted primarily from the acquisition of BDM and from
higher volume in the Automotive and Space, Defense & Information Systems
segments partially offset by a strong U.S. dollar and unfavorable pricing in
the Automotive segment. The higher operating profit was due to the higher sales
and continued cost-reduction efforts partially offset by higher research and
development expenditures, start-up costs and lower pricing in the Automotive
segment. First quarter 1998 earnings included a $31.5 million benefit from the
settlement of certain patent litigation, offset in part by $21.8 million in
charges for litigation and contract reserves and severance costs relating to
the combination of the Company's systems integration business with BDM.

Interest expense was $38 million for the first quarter of 1998, compared to $20
million for the first quarter of 1997, primarily due to financing the
acquisition of BDM.

Automotive
(In millions)
<TABLE>
<CAPTION>

                                                                                   First Quarter
                                                               -------------------------------------------------------
                                                                                                          Percent
                                                                      1998               1997            Inc(Dec)
                                                               ---------------    ----------------    ----------------

<S>                                                                 <C>                <C>              <C>
Sales                                                               $1,886             $1,793             5 %
Operating Profit                                                    $  147             $  167           (12)%
</TABLE>

The increase in sales resulted primarily from higher volume in most product
lines, particularly steering systems, seat belts and electronics, partially
offset by the effect of a strong U.S. dollar and lower pricing. The decline in
operating profit resulted in part from higher research and development and costs
associated with new product introductions and start-up facilities. The decline
in operating profit was also affected by the continuation of severe pricing
pressures. The Company is taking appropriate action with its customers to
mitigate the pressure on price as well as accelerate additional cost reduction
initiatives.



<PAGE>   11


Space, Defense & Information Systems
(In millions)
<TABLE>
<CAPTION>

                                                                                   First Quarter
                                                               -------------------------------------------------------
                                                                                                          Percent
                                                                      1998               1997            Inc(Dec)
                                                               ---------------    ----------------    ----------------

<S>                                                                 <C>                  <C>                <C>
Sales                                                               $1,209               $867               39%
Operating Profit                                                    $  115               $ 77               49%
</TABLE>

Sales increased due to the effect of the acquisition of BDM, which contributed
$232 million, new contract awards and higher volume in continuing programs. The
higher operating profit was due to the acquisition of BDM, continued success in
commercial gallium arsenide (GaAs) technology programs, and the benefit from the
settlement of certain patent litigation, which was offset in part by charges for
litigation and contract reserves and severance costs relating to the combination
of the Company's systems integration business with BDM.

LIQUIDITY AND FINANCIAL POSITION

In the first quarter of 1998, a net increase in debt of $470 million and a net
increase of $7 million in other items, were used to fund business acquisitions
of $228 million, capital expenditures of $119 million, reacquisition of common
stock of $24 million of which $5 million was for the settlement of shares
repurchased in 1997, dividend payments of $38 million and operating activities
of $46 million. As a result, cash and cash equivalents increased by $22 million.

Net debt (short-term debt, the current portion of long-term debt and long-term
debt less cash and cash equivalents) was $2,050 million at March 31, 1998,
compared to $1,586 million at December 31, 1997. The ratio of net debt to total
capital (net debt, minority interests and shareholders' investment) was 53.0
percent at March 31, 1998, compared to 47.8 percent at December 31, 1997.

During January 1998, the Company refinanced short-term debt by issuing $500
million of notes and debentures which mature at various dates through 2028.

During the first quarter 1998, the Company established a $1 billion Universal
Shelf Registration Statement. Securities that may be issued under this shelf
registration statement include: debt securities, common stock, warrants to
purchase debt securities and warrants to purchase common stock. No securities
were issued under this shelf registration statement during the first quarter.

As of the end of the first quarter 1998, $300 million of short-term debt was
reclassified to long-term debt as the Company intends to refinance the
borrowings on a long-term basis and has the ability to do so under its U.S.
revolving credit agreements.

During the first quarter of 1998, 350,810 shares of TRW common stock were
repurchased for approximately $19 million.


<PAGE>   12


Management believes that funds generated from operations and existing borrowing
capacity are adequate to fund the current share repurchase program and finance
planned growth, capital expenditures, working capital requirements including tax
requirements, company-sponsored research and development programs and dividend
payments to shareholders.


OTHER MATTERS

During 1997, TRW Vehicle Safety Systems Inc., a wholly owned subsidiary of the
Company, reported to ADEQ potential violations of the Arizona hazardous waste
law at its Queen Creek, Arizona facility for the possible failure to properly
label and dispose of wastewater that might be classified as hazardous waste. If
ADEQ initiates proceedings against the Company with respect to such matters, the
Company could be liable for penalties and fines and other relief. Management is
currently evaluating this matter and is unable to make a meaningful estimate of
the amount or range of possible liability, if any, at this time, although
management believes that the Company would have meritorious defenses.

During 1996, the Company was advised by the DOJ that it had been named as a
defendant in two lawsuits brought by a former employee and filed under seal in
1994 and 1995, respectively, in the United States District Court for the Central
District of California under the QUI TAM provisions of the civil False Claims
Act. The Company cannot presently predict the outcome of these lawsuits,
although management believes that their ultimate resolution will not have a
material effect on the Company's financial condition or results of operations.

Refer to the "Contingencies" footnote in the Notes to Financial Statements for
further discussion of these matters.

<PAGE>   13


FORWARD-LOOKING STATEMENTS

Statements in this filing that are not historical facts are forward-looking
statements, which involve risks and uncertainties that could affect the
Company's actual results. Information regarding the important factors that could
cause the Company's actual results to differ materially from the forward-looking
statements contained in this filing can be found in the Company's reports filed
with the Securities and Exchange Commission.



Item 3.      Quantitative and Qualitative Disclosures about Market Risk
             ----------------------------------------------------------


There have been no material changes in market risk exposures during the first
quarter of 1998 that affect the disclosures presented in the Company's Annual
Report to Shareholders for the year ended December 31, 1997.




<PAGE>   14
PART II. OTHER INFORMATION


Item 1.  Legal Proceedings.
         ------------------

         During 1996, the Company was advised by the DOJ that it had been named
as a defendant in two lawsuits brought by Richard D. Bagley, a former employee
of the Company's former Space & Technology Group, and originally filed under
seal in 1994 and 1995, respectively, in the United States District Court for the
Central District of California under the QUI TAM provisions of the civil False
Claims Act. The Act permits an individual to bring suit in the name of the
United States and share in any recovery. The allegations in the lawsuits relate
to the classification of costs incurred by the Company that were charged to
certain of its federal contracts. Under the law, the government must investigate
the allegations and determine whether it wishes to intervene and take
responsibility for the lawsuits. On February 13, 1998, the DOJ intervened in the
litigation. On February 19, 1998 and March 4, 1998, Bagley filed amended
complaints in the Central District of California that realleged certain of the
claims included in the 1994 and 1995 lawsuits and omitted the remainder. The
amended complaints allege that the United States has incurred substantial
damages and that the Company should be ordered to cease and desist from
violations of the civil False Claims Act and is liable for treble damages,
penalties, costs, including attorneys' fees, and such other relief as deemed
proper by the court. On March 17, 1998, the DOJ filed its complaint against the
Company upon intervention in the 1994 lawsuit, which set forth a limited number
of the allegations in the 1994 lawsuit and other allegations not in the 1994
lawsuit. The DOJ elected not to pursue the other claims in the 1994 lawsuit or
the claims in the 1995 lawsuit. The DOJ's complaint alleges that the Company is
liable for treble damages, penalties, interest, costs and "other proper relief."
On March 18, 1998, Bagley withdrew the first amended complaint in the 1994
lawsuit at the request of the DOJ. The Company expects to file responses to
Bagley's first amended complaint in the 1995 lawsuit and the DOJ's complaint
during the second quarter of 1998 and intends to defend itself vigorously. The
Company cannot presently predict the outcome of these lawsuits, although
management believes that their ultimate resolution will not have a material
effect on the Company's financial condition or results of operations.

         In 1992, Vinnell Mining & Minerals Corporation ("VMMC") and Atlas
Corporation ("Atlas"), an unrelated third party, entered into a Consent Decree
with the United States Environmental Protection Agency ("EPA") with respect to
an operable unit of the Atlas Asbestos Mine Superfund site in Fresno County, 
California. VMMC is a wholly owned indirect subsidiary of BDM International,
Inc. that was acquired by the Company in December 1997. The Consent Decree
provides, among other things, for the remediation of the site and reimbursement
of oversight costs upon submission of appropriate documentation to VMMC and
Atlas. On March 31, 1998, VMMC and Atlas filed a Motion to Enforce the Consent
Decree in the U.S. District Court for the Eastern District of California to
obtain judicial review of the oversight cost documentation requirements. On
April 6, 1998, the EPA issued a Statement of Decision stating that VMMC and
Atlas must pay the contested oversight costs, plus interest. The EPA has also
taken the position that VMMC and Atlas are subject to stipulated daily
penalties under the Consent Decree as of March 20, 1998. The Consent Decree
provides for maximum daily penalties of up to $6,250. Management believes that 
the ultimate resolution of this matter will not have a material effect on the
Company's financial condition or results of operations.


<PAGE>   15
Item 6.  Exhibits and Reports on Form 8-K.
         ---------------------------------

(a)      Exhibits:

         4.1        Indenture between TRW Inc. and The Chase Manhattan Bank 
                    (National Association), as successor Trustee, dated as of
                    May 1, 1986 (Exhibit 2 to TRW Form 8-A Registration
                    Statement dated July 3, 1986 is incorporated herein by
                    reference).

         4.2        First Supplemental Indenture between TRW Inc. and The Chase 
                    Manhattan Bank (National Association), as successor Trustee,
                    dated as of July 26, 1989 (Exhibit 4(b) to TRW Form S-3
                    Registration Statement, File No. 33-30350, is incorporated
                    herein by reference).

         27         Financial Data Schedule.

         99         Computation of Ratio of Earnings to Fixed Charges -- 
                    Unaudited (Supplement to Exhibit 12 of the following  
                    Form S-3 Registration Statements of the Company:  
                    No. 333-48443, filed March 23, 1998).

         Certain instruments with respect to long-term debt have not been filed
         as exhibits as the total amount of securities authorized under any one
         of such instruments does not exceed 10% of the total assets of the
         registrant and its subsidiaries on a consolidated basis. The registrant
         agrees to furnish to the Commission a copy of each such instrument upon
         request.


(b)      Reports on Form 8-K:

         Current Report on Form 8-K dated April 13, 1998 as to Medium-Term
         Notes.


SIGNATURES


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


                                    TRW Inc.



Date:  May 1, 1998                 By:  /s/ William B. Lawrence
                                        -----------------------
                                         William B. Lawrence
                                         Executive Vice President and Secretary


Date:  May 1, 1998                 By:  /s/ Carl G. Miller
                                        ------------------
                                         Carl G. Miller
                                         Executive Vice President
                                         and Chief Financial Officer


<PAGE>   16






                                    FORM 10-Q

                Quarterly Report for Quarter Ended March 31, 1998



                                  EXHIBIT INDEX
                                  -------------


EXHIBIT NO.            DESCRIPTION

       4.1        Indenture between TRW Inc. and The Chase Manhattan Bank 
                  (National Association), as successor Trustee, dated as of
                  May 1, 1986 (Exhibit 2 to TRW Form 8-A Registration
                  Statement dated July 3, 1986 is incorporated herein by
                  reference).

       4.2        First Supplemental Indenture between TRW Inc. and The Chase 
                  Manhattan Bank (National Association), as successor Trustee,
                  dated as of July 26, 1989 (Exhibit 4(b) to TRW Form S-3
                  Registration Statement, File No. 33-30350, is incorporated
                  herein by reference).

       27         Financial Data Schedule.

       99         Computation of Ratio of Earnings to Fixed Charges -- 
                  Unaudited (Supplement to Exhibit 12 of the following 
                  Form S-3 Registration Statements of the Company: No.
                  333-48443, filed March 23, 1998).