<PAGE>   1
 
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MARCH 17, 1999
================================================================================

                                   FORM 10-Q
 
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 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 JANUARY 31, 1999
 
                                       OR
 
      [ ]   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
        SECURITIES EXCHANGE ACT OF 1934
 
                         COMMISSION FILE NUMBER 1-3998
 
                            LITTON INDUSTRIES, INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 
<TABLE>
<S>                                            <C>
                   DELAWARE                                      95-1775499
       (STATE OR OTHER JURISDICTION OF                        (I.R.S. EMPLOYER
        INCORPORATION OR ORGANIZATION)                      IDENTIFICATION NO.)

           21240 BURBANK BOULEVARD,                              91367-6675
          WOODLAND HILLS, CALIFORNIA                             (ZIP CODE)
   (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)
</TABLE>
 
       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (818) 598-5000
 
     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 [ ]
 
     On February 26, 1999 there were 45,389,392 shares of Common Stock
outstanding.
 
                                  Page 1 of 14
 
                       Exhibit Index appears on Page 13.
 
================================================================================
<PAGE>   2
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                                     INDEX
 
                              REPORT ON FORM 10-Q
 
                       FOR QUARTER ENDED JANUARY 31, 1999
 
<TABLE>
<CAPTION>
                                                                          PAGE
                                                                         NUMBER
                                                                         ------
<S>        <C>                                                           <C>
PART I. FINANCIAL INFORMATION
 
  Item 1.  Financial Statements
 
           Consolidated Statements of Operations
             Six months ended January 31, 1999 and 1998................     3
 
           Consolidated Statements of Operations
             Three months ended January 31, 1999 and 1998..............     4
 
           Consolidated Balance Sheets
             January 31, 1999 and July 31, 1998........................     5
 
           Consolidated Statements of Cash Flows
             Six months ended January 31, 1999 and 1998................     6
 
           Notes to Consolidated Financial Statements..................     7
 
  Item 2.  Management's Discussion and Analysis of
             Financial Condition and Results of Operations.............     9
 
  Item 3.  Quantitative and Qualitative Disclosures About Market
             Risk......................................................    11
 
PART II. OTHER INFORMATION
 
  Item 1.  Legal Proceedings...........................................    12
 
  Item 4.  Submission of Matters to a Vote of Security Holders.........    13
 
  Item 6.  Exhibits and Reports on Form 8-K............................    13
 
Signature..............................................................    14
</TABLE>
 
                                        2
<PAGE>   3
 
                         PART I. FINANCIAL INFORMATION
 
ITEM 1. FINANCIAL STATEMENTS
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                (THOUSANDS OF DOLLARS, EXCEPT PER SHARE AMOUNTS)
 
<TABLE>
<CAPTION>
                                                                  SIX MONTHS ENDED
                                                                    JANUARY 31,
                                                              ------------------------
                                                                 1999          1998
                                                              ----------    ----------
<S>                                                           <C>           <C>
Sales and Service Revenues..................................  $2,338,460    $2,012,850
                                                              ----------    ----------
Costs and Expenses
  Cost of sales.............................................   1,829,583     1,541,224
  Selling, general and administrative.......................     244,426       240,659
  Depreciation and amortization.............................      79,934        69,559
  Interest -- net...........................................      32,509        21,299
                                                              ----------    ----------
          Total.............................................   2,186,452     1,872,741
                                                              ----------    ----------
Earnings before Taxes on Income.............................     152,008       140,109
Taxes on Income.............................................     (60,803)      (56,044)
                                                              ----------    ----------
Net Earnings................................................  $   91,205    $   84,065
                                                              ==========    ==========
Earnings per Share:
  Basic.....................................................  $     2.00    $     1.82
                                                              ==========    ==========
 
  Diluted...................................................  $     1.95    $     1.77
                                                              ==========    ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
                                        3
<PAGE>   4
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                (THOUSANDS OF DOLLARS, EXCEPT PER SHARE AMOUNTS)
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                                   JANUARY 31,
                                                              ----------------------
                                                                 1999         1998
                                                              ----------    --------
<S>                                                           <C>           <C>
Sales and Service Revenues..................................  $1,130,922    $973,815
                                                              ----------    --------
Costs and Expenses
  Cost of sales.............................................     884,374     741,207
  Selling, general and administrative.......................     116,900     118,668
  Depreciation and amortization.............................      40,096      35,171
  Interest  -- net..........................................      16,259      11,068
                                                              ----------    --------
          Total.............................................   1,057,629     906,114
                                                              ----------    --------
Earnings before Taxes on Income.............................      73,293      67,701
Taxes on Income.............................................     (29,317)    (27,081)
                                                              ----------    --------
Net Earnings................................................  $   43,976    $ 40,620
                                                              ==========    ========
Earnings per Share:
  Basic.....................................................  $     0.96    $   0.88
                                                              ==========    ========
 
  Diluted...................................................  $     0.94    $   0.86
                                                              ==========    ========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
                                        4
<PAGE>   5
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                          CONSOLIDATED BALANCE SHEETS
                             (THOUSANDS OF DOLLARS)
 
<TABLE>
<CAPTION>
                                                              JANUARY 31,     JULY 31,
                                                                 1999           1998
                                                              -----------    ----------
<S>                                                           <C>            <C>
ASSETS
Current Assets
  Cash and marketable securities............................  $   96,811     $   31,925
  Accounts receivable, net..................................     867,089        820,624
  Inventories less progress billings........................     629,793        635,942
  Deferred tax assets.......................................     410,886        417,719
  Prepaid expenses..........................................      27,611         27,770
                                                              ----------     ----------
          Total Current Assets..............................   2,032,190      1,933,980
                                                              ----------     ----------
Property, Plant and Equipment -- at cost....................   1,551,739      1,543,041
  Less accumulated depreciation.............................    (944,928)      (929,527)
                                                              ----------     ----------
Property, Plant and Equipment, Net..........................     606,811        613,514
                                                              ----------     ----------
Goodwill and Other Intangibles, Net.........................   1,050,638      1,075,299
                                                              ----------     ----------
Other Assets and Long-term Investments......................     458,888        427,022
                                                              ----------     ----------
          Total Assets......................................  $4,148,527     $4,049,815
                                                              ==========     ==========
 
LIABILITIES AND SHAREHOLDERS' INVESTMENT
Current Liabilities
  Accounts payable..........................................  $  786,146     $  876,850
  Payrolls and related expenses.............................     193,665        200,059
  Taxes on income...........................................      71,597         74,040
  Short-term debt...........................................     380,511        274,178
  Contract liabilities and customer deposits................     356,937        346,270
                                                              ----------     ----------
          Total Current Liabilities.........................   1,788,856      1,771,397
                                                              ----------     ----------
Long-term Obligations.......................................     775,410        771,321
                                                              ----------     ----------
Postretirement Benefit Obligations Other than Pensions......     206,556        206,397
                                                              ----------     ----------
Deferred Tax and Other Long-term Liabilities................     118,811        113,461
                                                              ----------     ----------
Shareholders' Investment
  Capital stock
     Voting preferred stock -- Series B.....................       2,053          2,053
     Common stock...........................................      45,429         45,783
  Additional paid-in capital................................     319,040        316,628
  Retained earnings.........................................     934,822        869,359
  Accumulated other comprehensive loss --
     Cumulative currency translation adjustment.............     (42,450)       (46,584)
                                                              ----------     ----------
          Total Shareholders' Investment....................   1,258,894      1,187,239
                                                              ----------     ----------
          Total Liabilities and Shareholders' Investment....  $4,148,527     $4,049,815
                                                              ==========     ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
                                        5
<PAGE>   6
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                             (THOUSANDS OF DOLLARS)
 
<TABLE>
<CAPTION>
                                                                SIX MONTHS ENDED
                                                                  JANUARY 31,
                                                              --------------------
                                                                1999        1998
                                                              --------    --------
<S>                                                           <C>         <C>
Cash and cash equivalents at beginning of period............  $ 16,175    $  4,144
                                                              --------    --------
Operating activities
  Net earnings..............................................    91,205      84,065
  Adjustments to reconcile net earnings to net cash provided
   by (used for) operating activities
     Depreciation and amortization..........................    79,934      69,559
     Changes in assets and liabilities
       Accounts receivable..................................   (49,359)    (40,061)
       Inventories..........................................    (9,789)     25,239
       Prepaid expenses.....................................        25       2,860
       Accounts payable.....................................   (89,876)    (65,749)
       Payrolls and related expenses........................   (15,280)     (2,346)
       Deferred and current taxes on income.................    10,070     (95,588)
       Contract liabilities and customer deposits...........    10,667     (14,076)
     Other operating activities.............................   (24,454)    (12,324)
                                                              --------    --------
Cash provided by (used for) operating activities............     3,143     (48,421)
                                                              --------    --------
Investing activities
  Proceeds from sale of business............................    45,990          --
  Purchase of capital assets................................   (55,262)    (42,799)
  Other investing activities................................   (10,448)    (15,654)
                                                              --------    --------
Cash used for investing activities..........................   (19,720)    (58,453)
                                                              --------    --------
Financing activities
  Change in short-term debt, net............................   104,977     112,544
  Purchase of Common stock..................................   (29,485)     (5,084)
  Other financing activities................................     2,381       3,832
                                                              --------    --------
Cash provided by financing activities.......................    77,873     111,292
                                                              --------    --------
Resulting in increase in cash and cash equivalents..........    61,296       4,418
                                                              --------    --------
Cash and cash equivalents at end of period..................  $ 77,471    $  8,562
                                                              ========    ========
Supplemental disclosure of cash flow information
  Interest paid.............................................  $ 35,016    $ 22,934
  Income taxes paid, net....................................  $ 48,954    $142,013
 
Reconciliation to Consolidated Balance Sheets:
  Cash and cash equivalents.................................  $ 77,471    $  8,562
  Marketable securities.....................................    19,340      15,750
                                                              --------    --------
          Total cash and marketable securities..............  $ 96,811    $ 24,312
                                                              ========    ========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
                                        6
<PAGE>   7
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                       SIX MONTHS ENDED JANUARY 31, 1999
 
     1. The amounts included in this report are unaudited; however, in the
        opinion of management, all adjustments necessary for a fair statement of
        results for the stated periods have been included. These adjustments are
        of a normal recurring nature. Certain information and footnote
        disclosures normally included in annual financial statements prepared in
        accordance with generally accepted accounting principles have been
        condensed or omitted. Certain reclassifications of prior period
        information were made for comparative purposes. These interim
        consolidated financial statements should be read in conjunction with the
        financial statements and notes thereto included in the Company's Annual
        Report to Shareholders for the fiscal year ended July 31, 1998. The
        results of operations for the six months ended January 31, 1999 are not
        necessarily indicative of operating results for the entire year.
 
     2. The components of inventory balances are summarized below:
 
<TABLE>
<CAPTION>
                                                   JANUARY 31, 1999    JULY 31, 1998
                                                   ----------------    -------------
                                                        (THOUSANDS OF DOLLARS)
<S>                                                <C>                 <C>
Raw materials and work in progress...............     $  996,785        $1,036,492
Finished goods...................................         50,964            42,746
                                                      ----------        ----------
                                                       1,047,749         1,079,238
Less progress billings...........................       (417,956)         (443,296)
                                                      ----------        ----------
Net inventories..................................     $  629,793        $  635,942
                                                      ==========        ==========
</TABLE>
 
     3. Interest (expense) income is shown below:
 
<TABLE>
<CAPTION>
                                   THREE MONTHS ENDED       SIX MONTHS ENDED
                                      JANUARY 31,             JANUARY 31,
                                  --------------------    --------------------
                                    1999        1998        1999        1998
                                  --------    --------    --------    --------
                                             (THOUSANDS OF DOLLARS)
<S>                               <C>         <C>         <C>         <C>
Interest expense................  $(18,364)   $(12,737)   $(36,405)   $(24,755)
Interest income.................     2,105       1,669       3,896       3,456
                                  --------    --------    --------    --------
Net interest expense............  $(16,259)   $(11,068)   $(32,509)   $(21,299)
                                  ========    ========    ========    ========
</TABLE>
 
     4. The Company computes basic and diluted earnings per share ("EPS") in
        accordance with the Statement of Financial Accounting Standards No. 128,
        "Earnings per Share" ("SFAS 128") which the Company adopted in the
        second quarter of fiscal year 1998. Basic EPS is calculated based on the
        weighted average number of shares outstanding and diluted EPS includes
        the effects of dilutive potential common shares.
 
                                        7
<PAGE>   8
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                       SIX MONTHS ENDED JANUARY 31, 1999
 
        The following table sets forth the computation of basic and diluted
earnings per share:
 
<TABLE>
<CAPTION>
                                 THREE MONTHS ENDED            SIX MONTHS ENDED
                                     JANUARY 31,                  JANUARY 31,
                              -------------------------    -------------------------
                                 1999          1998           1999          1998
                              -----------   -----------    -----------   -----------
                                 (THOUSANDS OF DOLLARS, EXCEPT PER SHARE AMOUNTS)
<S>                           <C>           <C>            <C>           <C>
Net earnings................  $    43,976   $    40,620    $    91,205   $    84,065
Preferred stock dividends...         (205)         (205)          (410)         (410)
                              -----------   -----------    -----------   -----------
Net earnings used for basic
  and diluted earnings per
  share calculations........  $    43,771   $    40,415    $    90,795   $    83,655
                              ===========   ===========    ===========   ===========
 
Weighted average common
  shares outstanding -- used
  for basic earnings per
  share.....................   45,465,074    46,087,621     45,506,917    46,059,790
Dilutive effect of stock
  options...................    1,056,304     1,180,035        995,586     1,178,416
                              -----------   -----------    -----------   -----------
Number of shares used for
  diluted earnings per
  share.....................   46,521,378    47,267,656     46,502,503    47,238,206
                              ===========   ===========    ===========   ===========
 
Basic earnings per share....  $      0.96   $      0.88    $      2.00   $      1.82
                              ===========   ===========    ===========   ===========
 
Diluted earnings per
  share.....................  $      0.94   $      0.86    $      1.95   $      1.77
                              ===========   ===========    ===========   ===========
</TABLE>
 
     5. Effective in the first quarter of fiscal year 1999, the Company adopted
        Statement of Financial Accounting Standards No. 130, "Reporting
        Comprehensive Income", which establishes standards for reporting and
        display of comprehensive income and its components. Comprehensive income
        includes "all changes in equity during a period except those resulting
        from investments by owners and distributions to owners".
 
        Comprehensive income and its components are summarized below:
 
<TABLE>
<CAPTION>
                                        THREE MONTHS ENDED     SIX MONTHS ENDED
                                           JANUARY 31,           JANUARY 31,
                                        ------------------    ------------------
                                         1999       1998       1999       1998
                                        -------    -------    -------    -------
                                                 (THOUSANDS OF DOLLARS)
<S>                                     <C>        <C>        <C>        <C>
Net earnings..........................  $43,976    $40,620    $91,205    $84,065
Currency translation adjustments......   (2,291)    (3,579)     4,134     (2,041)
                                        -------    -------    -------    -------
          Total.......................  $41,685    $37,041    $95,339    $82,024
                                        =======    =======    =======    =======
</TABLE>
 
                                        8
<PAGE>   9
 
                   PART I.  FINANCIAL INFORMATION (CONTINUED)
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS
 
     The Company reported sales of $1.13 billion and $2.34 billion for the
second quarter and six months ended January 31, 1999 compared with $973.8
million and $2.01 billion for the prior year's periods, respectively. Operating
profit improved to $104.9 million and $215.0 million for the second quarter and
six months ended January 31, 1999 compared with $92.2 million and $188.2 million
for the corresponding periods of the prior fiscal year. Net earnings rose 8.3%
to $44.0 million for the quarter and 8.5% to $91.2 million for the six months
ended January 31, 1999. Corresponding amounts for the fiscal year 1998 periods
were $40.6 million and $84.1 million, respectively.
 
     Sales and operating profit for the Advanced Electronics segment were $361.3
million and $26.9 million for the second quarter of fiscal year 1999, compared
with $365.0 million and $25.0 million for the second quarter of the prior year.
Sales and operating profit for the six months of the current fiscal year were
$764.5 million and $56.3 million compared with $778.3 million and $52.1 million
for the six months of fiscal year 1998. Although sales decreased slightly due to
the sale of a division in the first quarter, operating margins and profit
benefited from improved results on programs related to inertial navigation
components and products, the shift into the production phase on certain defense
electronics programs and ongoing cost containment efforts. Backlog for the
Advanced Electronics segment was $1.32 billion at January 31, 1999 compared with
$1.46 billion at July 31, 1998.
 
     The Information Systems segment reported sales and operating profit of
$396.0 million and $19.8 million for the second quarter of fiscal year 1999,
compared with $261.8 million and $15.1 million for the second quarter of the
prior year. For the first six months of the current fiscal year, sales and
operating profit were $792.8 million and $40.4 million compared with $514.8
million and $32.5 million for the same period of fiscal year 1998. These
improvements were primarily due to the acquisition of TASC, Inc. ("TASC") in
April 1998 and higher volume on various contracts at the Company's PRC Inc.
subsidiary which supplies information technology, services, systems integration
and technical support to federal, state and other customers. Profit margins for
this segment, however, continued to be impacted by investments in new programs
and costs incurred for the development of commercial information technology
services. Firm backlog for the Information Systems segment was $954.1 million at
January 31, 1999 compared with $877.7 million at July 31, 1998. In addition,
TASC and PRC have non-firm, unfunded backlog with potential contract values of
$2.0 billion at January 31, 1999 compared with $1.8 billion at July 31, 1998.
 
     The Marine Engineering and Production segment reported sales and operating
profit of $241.6 million and $34.1 million for the current quarter, compared
with $222.8 million and $29.1 million for the prior year's second quarter. The
respective amounts for the six months of fiscal year 1999 were $509.8 million
and $69.2 million compared with $461.4 million and $59.3 million for the six
months of fiscal year 1998. These increases reflect a higher level of
construction activities on long-term contracts, partially offset by the effects
of the completion and delivery of an Aegis destroyer and a sixth LHD class
amphibious assault ship during the second half of fiscal year 1998. During the
current quarter, the Company completed and delivered another Aegis destroyer to
the Navy. Operating margins benefited from increased earnings rates on programs
maturing in the production process and continued production efficiencies.
Backlog for this segment increased to $3.73 billion at January 31, 1999 from
$3.47 billion at July 31, 1998 mainly due to the exercise of an option by the
U.S. Navy during the second quarter to build two additional destroyers worth
over $600 million. Subsequent to the end of the quarter, the Company signed a
contract with American Classic Voyages Co. to build two passenger cruise ships
with an option for a third vessel with an aggregate potential value of $1.4
billion. The Company is also undertaking an effort to update facilities and
improve production capabilities and expects to spend approximately $130 million
over the next two years.
 
     The Electronic Components and Materials segment reported sales and
operating profit of $144.0 million and $24.6 million for the second quarter of
the current fiscal year compared with $139.7 million and $23.7 million for the
same period of the prior year. Sales and operating profit for the six months of
the current fiscal year were $296.2 million and $50.4 million compared with
$286.9 million and $45.8 million for the six
 
                                        9
<PAGE>   10
                   PART I.  FINANCIAL INFORMATION (CONTINUED)
 
months of fiscal year 1998. In response to demand for its commercial electronic
products by original equipment manufacturers in the telecommunications and
computer industries, this segment has continued to invest in product development
and expand production capacity. Profit margins benefited from management's
ongoing program to improve process and cost efficiencies.
 
     Net interest expense for the second quarter and six months ended January
31, 1999 amounted to $16.3 million and $32.5 million compared with $11.1 million
and $21.3 million for the prior year's periods, respectively. Interest expense
was higher in the current year primarily as a result of the $300 million in
certain long-term notes and debentures along with short-term borrowings issued
in connection with the acquisition of TASC and a payment of prior years' taxes
during fiscal year 1998.
 
     Cash and marketable securities amounted to $96.8 million at January 31,
1999 compared with $31.9 million at July 31, 1998. During the current six month
period, cash flow from operations, short-term borrowings and proceeds from the
sale of a division provided the funds to meet operating needs, make capital
expenditures and repurchase 537,100 shares of Common stock for approximately
$29.5 million in cash, leaving approximately 1.6 million shares to be
repurchased under the Company's stock buyback program as of January 31, 1999. At
January 31, 1999, the Company had credit commitments totaling $400 million of
which approximately $200 million was available for its general use and the
remainder for replacement of existing debt. The Company also has another
revolving credit agreement totaling $400 million which serves as a back-up
facility for its commercial paper program under which $342.5 million was
outstanding at January 31, 1999. The aforementioned credit commitments, along
with available cash, provided the funds for the previously announced
acquisitions of Denro, Inc. from Firan Corporation and Retconn, Inc. from SEMX
Corporation, both of which were completed subsequent to the end of the current
quarter. Management believes that cash flow from operations, along with
available borrowing capacity, will be sufficient to meet operating requirements.
 
EURO CONVERSION
 
     On January 1, 1999, a majority of the European Union member countries
converted to a common currency, the "Euro". The existing national currencies of
the participating countries will continue to be acceptable until January 1, 2002
after which the Euro will be the sole legal tender for the participating
countries. The Company is currently evaluating the economic and operational
impact, including competition, pricing, contracts, taxation and foreign currency
exchange rate risk, of the Euro conversion but does not expect it to have a
material effect on its financial condition or results of operations.
 
YEAR 2000 READINESS DISCLOSURES
 
     The Company has developed plans and a program to address the potential
impact of the Year 2000 on its business systems, facilities and products which
may include imbedded software. Each of these areas has been inventoried for
potential Year 2000 impact. Detailed implementation plans are in place for the
required modifications or replacements and such plans are being reviewed and
tested. The process and progress is monitored on a regular basis by a special
corporate task group of management, internal audit and legal personnel and
reported to management and the Audit and Compliance Committee of the Board of
Directors. Implementation of the required changes to critical systems,
facilities and products is expected to be completed during fiscal year 1999. The
Company is in contact with major suppliers and customers and is developing
backup and contingency plans both in relation to internal systems, facilities
and products and third parties. Incremental costs to address and achieve Year
2000 compliance are expensed as incurred. Such costs are approximately $14
million through January 31, 1999 and expected to total approximately $24
million. In addition, the Company has continued its process of replacing
manufacturing and business systems with more efficient and technologically up to
date systems that are also Year 2000 compliant. The Company believes it is
taking reasonable steps to prevent a material adverse operational or financial
impact from a non-compliant situation. The effect, if any, on the Company's
results of operations if the Company or any of its customers or suppliers is not
Year 2000 compliant is not reasonably estimable.
                                       10
<PAGE>   11
                   PART I.  FINANCIAL INFORMATION (CONTINUED)
 
SAFE HARBOR CAUTIONARY STATEMENT
 
     Certain statements contained in this document are "forward-looking
statements" within the meaning of The Private Securities Reform Act of 1995. For
this purpose, any statements contained herein that are not statements of
historical fact may be deemed to be forward-looking statements. Without limiting
themselves to the foregoing, the words "believes", "anticipates", "estimates",
"expects", and similar expressions are intended to identify forward-looking
statements. Such forward-looking statements involve known and unknown risks and
uncertainties that could cause the Company's actual actions or results to differ
materially from those discussed in the forward-looking statements. Specific
factors that might cause such a difference include, but are not limited to,
changing priorities or reductions in the U.S. government defense budget; the
Company's reliance on U.S. Navy contracts; and profit recognition on government
and commercial contracts. The Company does not undertake any obligation to
publicly release any revisions to forward-looking statements to reflect events
or circumstances or changes in expectations after the date of this document or
to reflect the occurrence of unanticipated events.
 
ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK
 
     See Part II, Item 7, "Management's Discussion and Analysis of Financial
Condition and Results of Operations", of the Company's Annual Report on Form
10-K for the fiscal year ended July 31, 1998 for a discussion of its exposure to
market risks. There has been no significant change during the six months ended
January 31, 1999.
 
                                       11
<PAGE>   12
 
                          PART II.  OTHER INFORMATION
 
ITEM 1. LEGAL PROCEEDINGS
 
     Litton brought suit against Honeywell, Inc. ("Honeywell") for patent
infringement relating to the manufacture of ring laser gyro navigation systems
used in commercial aircraft. In August 1993, the jury rendered a verdict in
favor of Litton which the District Court rejected in January 1995. In July 1996,
the Federal Circuit Court of Appeals reversed the District Court's decision and
reinstated parts of the jury's verdict related to liability in favor of Litton
and ordered a new trial on the amount of damages. In March 1997, the U.S.
Supreme Court vacated the Court of Appeals' ruling and remanded the case to the
Court of Appeals for further consideration. On April 7, 1998, the Court of
Appeals reinstated its finding that the patent was valid, reversed in part, and
ordered a new trial on both liability and damages. A new trial date has not been
set.
 
     Litton also brought suit against Honeywell for illegal monopolization of
the market for inertial reference systems for large commercial air transport,
commuter and business aircraft. In February 1996, a jury rendered a verdict in
favor of Litton. The District Court upheld the jury's verdict on liability, but
declined to enter the jury's damage award on the basis that Litton's damage
study did not disaggregate damages among legal and illegal conduct. A new trial
limited to the issue of the amount of damages resulted in a jury verdict on
December 9, 1998, in the amount of $250 million in favor of Litton. On January
27, 1999, U.S. District Court Judge Mariana R. Pfaelzer entered a final judgment
against Honeywell in the amount of $750 million plus post judgment interest from
the date of entry of the final judgment and costs and attorneys fees. The court
will review post trial motions of the parties and hold a hearing as soon after
May 3, 1999 as is consistent with the Court's calendar. Honeywell has stated
that it intends to appeal the judgment.
 
     At meetings and discussions in February 1999, the United States Attorney's
Office for the Central District of California ("the Government") advised the
Company that it intended to bring criminal charges against the Company and
potentially against some present and former officers and employees as a result
of a lengthy investigation of the Company's payments to foreign consultants and
the reporting of those payments to the United States Government in connection
with sales to Taiwan, Greece and possibly South Korea. While the Company
believes it has good and meritorious defenses to the potential charges, the
verdict in any trial cannot be predicted with certainty. The potential
administrative action also must be considered by the Company. As a result the
Company cannot at this time project the outcome and anticipates further
discussions with the Government.
 
                                       12
<PAGE>   13
                    PART II.  OTHER INFORMATION (CONTINUED)
 
ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS
 
     The Registrant's 1998 Annual Meeting of Shareholders was held on December
3, 1998 in Beverly Hills, California.
 
     Proxies for the meeting were solicited on behalf of the Board of Directors
of the Company. There was no solicitation in opposition to the Board of
Directors' nominees for election of directors as listed in the Company's
definitive Proxy Statement dated October 30, 1998. All of the nominees were
elected as follows:
 
<TABLE>
<CAPTION>
                   NOMINEE                         FOR        WITHHELD
                   -------                      ----------    --------
<S>                                             <C>           <C>
Alton J. Brann................................  40,639,580    207,471
Michael R. Brown..............................  40,644,423    202,628
Joseph T. Casey...............................  40,626,047    221,004
Carol B. Hallett..............................  40,720,021    127,030
Orion L. Hoch.................................  40,623,862    223,189
David E. Jeremiah.............................  40,724,010    123,041
John M. Leonis................................  40,641,663    205,388
William P. Sommers............................  40,723,571    123,480
C. B. Thornton, Jr. ..........................  40,728,667    118,384
</TABLE>
 
     In addition to electing directors, the shareholders voted to ratify the
appointment of Deloitte & Touche LLP as independent auditors by the following
votes: 40,761,987 shares "for", 49,269 shares "against", and 35,795 shares
"abstained"; and approve the Litton Industries, Inc. Non-Employee Director Stock
Plan by the following votes: 38,269,292 shares "for", 2,446,745 shares
"against", 130,514 shares "abstained" and 500 shares of "broker non-votes".
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
(a) Exhibits
 
<TABLE>
    <S>                         <C>
           Exhibit 3.2:         Amendment to Restated and Amended By-laws of the Company, as
                                adopted by the Board of Directors on January 14, 1999.
           Exhibit 27:          Financial Data Schedule.
                 
</TABLE>
 
(b) Reports on Form 8-K: There were no reports on Form 8-K filed during the
    second quarter ended January 31, 1999.
 
                                       13
<PAGE>   14
 
                                   SIGNATURE
 
     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.
 
                                          LITTON INDUSTRIES, INC.
                                          (Registrant)
 
                                          By      /s/ CAROL A. WIESNER
 
                                            ------------------------------------
                                                      Carol A. Wiesner
                                               Vice President and Controller
                                                 (Chief Accounting Officer)
 
March 17, 1999
 
                                       14