<PAGE>   1
 
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                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
                            ------------------------
 
                                   FORM 10-Q
 
(Mark One)
 
[X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
    ACT OF 1934
 
For the quarterly period ended October 2, 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 1-7006
 
                               BRUSH WELLMAN INC.
               (EXACT NAME OF REGISTRANT AS SPECIFIED IN CHARTER)
 
<TABLE>
<S>                                                           <C>
                            OHIO                                           34-0119320
      (STATE OR OTHER JURISDICTION OF INCORPORATION OR        (I.R.S. EMPLOYER IDENTIFICATION NO.)
                       ORGANIZATION)
</TABLE>
 
<TABLE>
<S>                                      <C>
 17876 ST. CLAIR AVENUE, CLEVELAND,         44110
                OHIO
    (ADDRESS OF PRINCIPAL EXECUTIVE      (ZIP CODE)
              OFFICES)
</TABLE>
 
                                  216-486-4200
               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 November 6, 1998 there were 16,380,610 shares of Common Stock, par
value $1 per share, outstanding.
 
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<PAGE>   2
 
                         PART I   FINANCIAL INFORMATION
 
                      BRUSH WELLMAN INC. AND SUBSIDIARIES
 
ITEM 1.   FINANCIAL STATEMENTS
 
     The consolidated financial statements of Brush Wellman Inc. and its
subsidiaries for the quarter ended October 2, 1998 are as follows:
 
          Consolidated Statements of Income -- Nine months ended October 2, 1998
     and September 26, 1997
 
          Consolidated Balance Sheets -- October 2, 1998 and December 31, 1997
 
          Consolidated Statements of Cash Flows -- Nine months ended October 2,
     1998 and September 26, 1997
 
                                        1
<PAGE>   3
 
CONSOLIDATED STATEMENTS OF INCOME
 
(UNAUDITED)
 
<TABLE>
<CAPTION>
                                                              THIRD QUARTER ENDED          NINE MONTHS ENDED
                                                           -------------------------   --------------------------
                                                             OCT. 2,      SEPT. 26,      OCT. 2,       SEPT. 26,
(DOLLARS IN THOUSANDS EXCEPT SHARE AND PER SHARE AMOUNTS)     1998          1997          1998           1997
-----------------------------------------------------------------------------------------------------------------
<S>                                                        <C>           <C>           <C>            <C>
Net sales........................................          $    96,240   $   109,073   $   313,414    $   322,135
  Cost of sales..................................               76,824        81,845       248,454        239,430
                                                           -----------   -----------   -----------    -----------
Gross Margin.....................................               19,416        27,228        64,960         82,705
  Selling, administrative and general expenses...               15,422        18,531        48,203         51,091
  Research and development expenses..............                2,185         2,013         6,357          5,573
  Other-net......................................                1,318         1,103        19,979            599
                                                           -----------   -----------   -----------    -----------
Operating Profit.................................                  491         5,581        (9,579)        25,442
  Interest expense...............................                  352            18           760            382
                                                           -----------   -----------   -----------    -----------
Income before income taxes.......................                  139         5,563       (10,339)        25,060
  Income taxes...................................                   41         1,574        (3,515)         7,092
                                                           -----------   -----------   -----------    -----------
Net Income.......................................          $        98   $     3,989   $    (6,824)   $    17,968
                                                           ===========   ===========   ===========    ===========
Per Share of Common Stock: Basic.................          $      0.01   $      0.25   $     (0.42)   $      1.11
Weighted average number of common shares outstanding...     16,197,162    16,238,666    16,295,836     16,191,303
Per Share of Common Stock: Diluted...............          $      0.01   $      0.24   $     (0.42)   $      1.10
Weighted average number of common shares outstanding...     16,252,643    16,529,359    16,295,836     16,386,371
Cash dividends per common share..................          $      0.12   $      0.12   $      0.36    $      0.34
</TABLE>
 
See notes to consolidated financial statements.
                                        2
<PAGE>   4
 
CONSOLIDATED BALANCE SHEETS
 
(UNAUDITED)
 
<TABLE>
<CAPTION>
                                                              OCT. 2,     DEC. 31,
(DOLLARS IN THOUSANDS)                                          1998        1997
----------------------------------------------------------------------------------
<S>                                                           <C>         <C>
ASSETS
Current Assets
  Cash and cash equivalents.................................  $  3,414    $  7,170
  Accounts receivable.......................................    63,644      62,812
  Inventories...............................................    99,621      90,714
  Prepaid expenses and other current assets.................    19,763      18,215
                                                              --------    --------
          Total Current Assets..............................   186,442     178,911
Other Assets................................................    34,970      31,319
Property, Plant and Equipment...............................   429,098     463,689
  Less allowances for depreciation, depletion and
     impairment.............................................   253,451     290,067
                                                              --------    --------
                                                               175,647     173,622
                                                              --------    --------
                                                              $397,059    $383,852
                                                              ========    ========
LIABILITIES AND SHAREHOLDERS' EQUITY
Current Liabilities
  Short-term debt...........................................  $ 66,584    $ 28,877
  Accounts payable..........................................    10,572      13,519
  Other liabilities and accrued items.......................    30,210      28,580
  Dividends payable.........................................         0       1,967
  Income taxes..............................................     4,064       5,369
                                                              --------    --------
          Total Current Liabilities.........................   111,430      78,312
Other Long-Term Liabilities.................................     6,886       8,200
Retirement and Post-Employment Benefits.....................    39,671      39,825
Long-Term Debt..............................................    17,105      17,905
Deferred Income Taxes.......................................      (358)      2,797
Shareholders' Equity........................................   222,325     236,813
                                                              --------    --------
                                                              $397,059    $383,852
                                                              ========    ========
</TABLE>
 
See notes to consolidated financial statements.
                                        3
<PAGE>   5
 
CONSOLIDATED STATEMENTS OF CASH FLOWS
 
(UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                NINE MONTHS ENDED
                                                              ---------------------
                                                              OCT. 2,     SEPT. 26,
(DOLLARS IN THOUSANDS)                                          1998        1997
-----------------------------------------------------------------------------------
<S>                                                           <C>         <C>
NET INCOME..................................................  $ (6,824)   $ 17,968
ADJUSTMENTS TO RECONCILE NET INCOME TO NET CASH PROVIDED
  FROM OPERATING ACTIVITIES:
  Depreciation, depletion and amortization..................    17,334      13,012
  Amortization of mine development..........................     2,792           1
  Decrease (Increase) in accounts receivable................      (594)    (22,657)
  Decrease (Increase) in Inventory..........................    (7,842)      4,200
  Decrease (Increase) in prepaid and other current assets...    (1,735)     (1,872)
  Increase (Decrease) in accounts payable and accrued
     expenses...............................................    (1,727)      8,990
  Increase (Decrease) in interest and taxes payable.........    (1,538)     (2,472)
  Increase (Decrease) in deferred income tax................    (3,155)        438
  Increase (Decrease) in other long-term liabilities........      (718)      1,590
  Impairment of fixed assets and related intangibles........    14,273          --
  Other -- net..............................................       458         (10)
                                                              --------    --------
     NET CASH PROVIDED FROM OPERATING ACTIVITIES............    10,724      19,188
CASH FLOWS FROM INVESTING ACTIVITIES:
  Payments for purchase of property, plant and equipment....   (29,267)    (38,918)
  Payments for mine development.............................      (294)     (9,398)
  Proceeds from (Payments for) other investments............   (12,003)        883
                                                              --------    --------
     NET CASH USED IN INVESTING ACTIVITIES..................   (41,564)    (47,433)
CASH FLOWS FROM FINANCING ACTIVITIES:
  Proceeds from issuance of short-term debt.................    38,254       7,829
  Repayment of short-term debt..............................      (528)        (93)
  Proceeds from issuance of long-term debt..................        --          --
  Repayment of long-term debt...............................      (800)       (960)
  Issuance of Common Stock under stock option plans.........     3,433       4,118
  Purchase of Common Stock for treasury.....................    (5,390)     (2,038)
  Payments of dividends.....................................    (7,837)     (5,343)
                                                              --------    --------
     NET CASH PROVIDED FROM FINANCING ACTIVITIES............    27,132       3,513
Effects of Exchange Rate Changes............................       (48)        (63)
                                                              --------    --------
     NET CHANGE IN CASH AND CASH EQUIVALENTS................    (3,756)    (24,795)
     CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD.......     7,170      31,749
                                                              --------    --------
  CASH AND CASH EQUIVALENTS AT END OF PERIOD................  $  3,414    $  6,954
                                                              ========    ========
</TABLE>
 
See notes to consolidated financial statements.
                                        4
<PAGE>   6
 
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
 
(UNAUDITED)
 
NOTE A -- ACCOUNTING POLICIES
 
     In management's opinion, the accompanying consolidated financial statements
contain all adjustments necessary to present fairly the financial position as of
October 2, 1998 and December 31, 1997 and the results of operations for the nine
months ended October 2, 1998 and September 26, 1997.
 
NOTE B -- INVENTORIES
 
<TABLE>
<CAPTION>
                                                              OCT. 2,    DEC. 31,
                   (DOLLARS IN THOUSANDS)                      1998        1997
---------------------------------------------------------------------------------
<S>                                                           <C>        <C>
Principally average cost:
  Raw materials and supplies................................  $18,357    $17,331
  In Process................................................   64,094     58,666
  Finished..................................................   38,820     37,008
                                                              -------    -------
                                                              121,271    113,005
Excess of average cost over LIFO inventory value............   21,650     22,291
                                                              -------    -------
                                                              $99,621    $90,714
                                                              =======    =======
</TABLE>
 
NOTE C -- COMPREHENSIVE INCOME
 
     As of January 1, 1998, the Company adopted Statement 130, "Reporting
Comprehensive Income". Statement 130 establishes new rules for the reporting and
display of comprehensive income and its components; however, the adoption of
this statement had no impact on the Company's net income or shareholders'
equity. Statement 130 requires certain items, including foreign currency
translation adjustments, which prior to adoption were reported separately in
shareholders' equity, to be included in other comprehensive income. Prior year
financial statements have been reclassified to conform to the requirements of
Statement 130.
 
     For the third quarter 1998 and 1997, comprehensive income/(loss) amounted
to $566,372 and $3,142,417, respectively. Year to date 1998 and 1997
comprehensive income/(loss) amounted to ($7,002,160) and $17,159,390,
respectively. The difference between net income/(loss) and comprehensive
income/(loss) is the cumulative translation adjustment for the periods
presented.
 
NOTE D -- SPECIAL CHARGE
 
     In the third quarter 1998, the Company recorded special charges totaling
$0.7 million pre-tax and $0.5 million after-tax for additional depreciation
charges on equipment that is scheduled to be taken out of service with the
planned completion of certain capital projects by December 31, 1998. This amount
was charged to Cost of sales on the consolidated income statement for the third
quarter 1998. Year to date special charges total $22.5 million pre-tax and $16.1
million after-tax as charges were booked in the second quarter 1998 primarily
for write-downs of property, plant and equipment, inventory and goodwill, and
increases to environmental reserves. Of the $22.5 million, $5.6 million was
charged to Cost of sales and $16.9 million was charged to Other-net on the
consolidated income statement for the nine month period ending October 2, 1998.
 
     In analyzing the strategic plans for each of the Company's business units,
management determined that the carrying value of certain assets within its
Microelectronics and Metal Systems Groups were impaired based upon current cash
flow projections. Property, plant and equipment and related intangibles with a
carrying value of $19.6 million was written down by $14.3 million to its
estimated fair market value in the second quarter 1998. The fair market value
was determined by a discounted cash flow analysis using the Company's estimated
pre-tax weighted average cost of capital. The impaired assets may be held for
future use. The $14.3 million impairment is included in Other-net on the
consolidated income statement for the nine month period ending October 2, 1998.
 
                                        5
<PAGE>   7
 
Inventory write-downs and certain provisions were also taken in the second
quarter 1998 as a result of the reduced market growth expectations and current
market conditions.
 
NOTE E -- NEW PRONOUNCEMENT
 
     In June 1998, the Financial Accounting Standards Board issued Statement No.
133, Accounting for Derivative Instruments and Hedging Activities, which is
required to be adopted in years beginning after June 15, 1999. The Statement
permits early adoption as of the beginning of any fiscal quarter after its
issuance. The Statement will require the Company to recognize all derivatives on
the balance sheet at fair value. Derivatives that are not hedges must be
adjusted to fair value through income. If the derivative is a hedge, depending
on the nature of the hedge, changes in the fair value of derivatives will either
be offset against the change in fair value of the hedged assets, liabilities, or
firm commitments through earnings or recognized in other comprehensive income
until the hedged item is recognized in earnings. The ineffective portion of a
derivative's change in fair value will be immediately recognized in earnings.
The Company has not yet determined when it will adopt the Statement nor has it
determined what the effect of the Statement will be on earnings and the
financial position of the Company.
 
                                        6
<PAGE>   8
 
ITEM 2.   MANAGEMENT'S DISCUSSION AND ANALYSIS
 
FORWARD-LOOKING INFORMATION
 
     Portions of narrative set forth in this document that are not historical in
nature are forward-looking statements. The Company's actual future performance
may differ from that contemplated in the forward-looking statements as a result
of a variety of factors that include, in addition to those mentioned elsewhere
herein, the condition of the markets which the Company serves (especially as
impacted by events in particular markets, including telecommunications,
automotive and electronics, or in particular geographic regions, such as Asia),
the success of the Company's strategic plans, the timely and successful
completion of pending capital expansions and the conclusion of pending
litigation matters in accordance with the Company's expectation that there will
be no materially adverse effects.
 
RESULTS OF OPERATIONS
 
     Sales in the third quarter 1998 were $96.3 million compared to $109.0
million in the third quarter 1997. Sales from both the Metal System Group and
Microelectronic Group were lower than last year; however, while Metal Systems'
profitability declined from the third quarter 1997, Microelectronics'
profitability increased. In addition to the results from normal operations, the
Company recorded a special charge of $0.7 million pre-tax that reduced diluted
earnings per share by $0.03 in the third quarter 1998.
 
     Sales from the Metal Systems Group, which includes alloy strip, alloy bulk,
engineered material systems and beryllium products, declined in the third
quarter 1998 from the third quarter 1997 due to the slowdown in Asian and U.S.
electronics markets, start-up issues with the alloy expansion project that
resulted in product flow constraints, the relatively strong dollar and the
General Motors strike. Metal Systems Group sales accounted for 71% of total
sales in the third quarter 1998.
 
     Alloy strip and engineered material system sales decreased in the third
quarter 1998 from the third quarter 1997 due to soft demand from two key markets
-telecommunications and electronics. This was evident not only domestically but
more so in Asia, where the weak economic conditions have caused a major downturn
in sales volumes. Automotive is also a major market for these products and the
General Motors strike adversely affected sales in the third quarter 1998. The
Company's strategy for these products remains to fully develop either new
applications or replace competing materials in existing applications in the
telecommunications, electronics and automotive markets.
 
     Sales of alloy bulk products, primarily copper beryllium alloys in plate,
rod, bar and tube form, were down from the prior year as a result of soft demand
from the aerospace, mold and oil and gas markets. The Company is actively
investing in new products and processes in order to expand its share in these
markets.
 
     Sales of beryllium products, which are a smaller portion of Metal Systems,
improved over third quarter 1997. These products service the aerospace and
defense markets.
 
     Sales from the Microelectronics Group, which includes precious metal
products from Williams Advanced Materials (WAM), ceramics and thick film
circuits, were less in the third quarter 1998 than in the third quarter 1997.
WAM's sales were lower due to a planned substitution of silver for gold in a
major application, as precious metal is a straight pass through to the customer.
The increased volume provided increased value added and profitability for the
current period as compared to the third quarter of last year. The acquisition of
Pure Tech Inc. a manufacturer of non-precious metal physical vapor deposition
material by WAM in the late second quarter 1998 provided additional sales and
profits in the third quarter of 1998.
 
     Ceramic sales declined in the third quarter 1998 from the prior year period
as a result of softening demand in the telecommunications market and the General
Motors strike. A new powder metallurgy operation at the Company's Tucson,
Arizona plant is anticipated to be placed in service in the fourth quarter 1998
and is designed to expand the Company's market opportunities.
 
     Thick film circuit sales were a minor portion of total sales and
essentially were unchanged from last year as a major government-supported
application has not developed as rapidly as anticipated.
 
                                        7
<PAGE>   9
 
     Year-to-date sales were $313.4 million in 1998 compared to $322.1 million
in 1997. Metal System sales increased 1% from last year as sales in the first
half 1998 were strong, compensating for the shortfall in the third quarter.
Microelectronic Group sales were 14% lower in the first nine months of 1998 than
in 1997 primarily as a result of the substitution of silver for gold in certain
precious metal applications. The weakening demand in the telecommunications and
electronics markets and the Asian economic slow down became evident in the
second quarter 1998 and continue to affect the Company into early fourth quarter
1998. The General Motors strike, while resolved in the third quarter, adversely
affected both the second and third quarter 1998 sales and profits. The stronger
U.S. dollar, as compared to last year, has also unfavorably impacted the current
year sales.
 
     International sales of all products were $89.7 million in the first nine
months of 1998, a 1% improvement over 1997, despite the strengthening dollar
which reduced the translated value of the Company's foreign sales as compared to
the prior period. Sales into Europe, particularly alloy strip products, have
increased in 1998 over 1997 while sales in Asia declined. The Company sells its
products internationally through a network of captive distribution centers and
outside distributors and agents. The international markets served are generally
the same as the domestic markets. The dollar's value against the yen weakened
considerably in the early part of the fourth quarter and in general, all else
equal, a weaker dollar typically results in a higher translated value of foreign
sales.
 
     Gross margin was $19.4 million or 20.1% of sales in the third quarter 1998
compared to $27.2 million or 25.0% of sales in the third quarter 1997. Start-up
costs and related manufacturing issues with the alloy expansion project in
Elmore, Ohio and the new facility in Lorain, Ohio have been greater than
initially anticipated and have negatively impacted margins. The fixed cost
component of Cost of sales has increased from last year as a result of these and
other investments through higher charges for depreciation, rent, insurance and
taxes. The adverse currency effect also contributed to the lower margin
percentage in the third quarter 1998. Included in Cost of sales for the third
quarter 1998 is $0.7 million of the special charge further explained below.
 
     For the first nine months of 1998 gross margin was $65.0 million or 20.7%
of sales compared to $82.7 million or 25.6% of sales in 1997. The factors
affecting margins in the third quarter apply to the first nine months as well.
The 1998 year-to-date special charge in Cost of sales is $5.6 million; absent
this charge, the 1998 gross margin would be 22.5%. The majority of the remaining
$12.1 million year-on-year margin decline is in the Metal Systems Group.
 
     Selling, administrative and general expenses were $15.4 million or 16.0% of
sales in the third quarter 1998 versus $18.5 million or 16.9% of sales in the
third quarter 1997. Year-to-date, these expenses were $48.2 million or 15.3% of
sales in 1998 and $51.1 million or 15.9% of sales in 1997. The somewhat
favorable comparisons result in part from development work for the new Lorain,
Ohio business venture incurred in 1997 and not in 1998 and the reclassification
of certain distribution expenses into product costs beginning in 1998. The
expense for employee incentive compensation plans is lower in 1998 than 1997.
The currency effect on expenses is also favorable in the current year as the
stronger dollar reduces the translated value of foreign currency expenses. This
translation benefit on expenses is significantly smaller than the unfavorable
translation impact on sales.
 
     The Company is undertaking several major capital investments to replace a
large portion of its legacy computer systems while other systems will be
undergoing major upgrades. One of the benefits from these system replacements
and upgrades is mitigating the need to make numerous legacy systems year 2000
compliant. The Company currently is actively addressing the year 2000 compliance
issue, for both information technology and non-information technology equipment
and systems, and estimates that the related expense will be approximately $1.0
million in 1998 with a smaller but undetermined amount anticipated to be
expensed in 1999. Outside consultants have been contracted to assist in
assessing the Company's exposure and costs. The majority of the sales, financial
and payroll information technology systems either already are or are anticipated
to be year 2000 compliant by the first quarter 1999, while the Company is in the
assessment phase relative to remediation of any year 2000 issues with its
non-information technology equipment. If required modifications and conversions
are not made on a timely basis, the year 2000 issue could have a material
adverse effect on the Company's operations. The Company can provide no assurance
that year 2000 compliance plans will be successfully completed by suppliers and
customers in a timely manner, nor has the Company been able to assess the
potential impact of noncompliance by any supplier or customer. While the Company
is attempting to resolve its year 2000 issues to the best of its understanding,
given the complexity of the issue and the potential costs, the Company
 
                                        8
<PAGE>   10
 
cannot provide absolute assurance that this issue will not have any impact on
the Company's future cash flows or results of operations. The Company
anticipates developing contingency plans as warranted.
 
     Research and development (R&D) expenses were $2.2 million in the third
quarter 1998 and $2.0 million in the third quarter of 1997. R&D expenses of $6.4
million for the first nine months of 1998 were $0.8 million higher than the
comparable period last year. Current major projects and the major causes for the
year-on-year increase include the development of new alloy system and refinement
of alloy casting processes and technologies.
 
     Other-net expense was $1.3 million in the third quarter 1998, a $0.2
million increase over the third quarter 1997. This category includes precious
metal consignment fees, amortization of intangibles, bad debts, exchange gains
and losses, interest income and other miscellaneous income and expense items.
 
     Other-net expense was $20.0 million for the first nine months of 1998
compared to $0.6 million in 1997. Included in the 1998 year-to-date Other-net
expense is $16.9 million of the $22.5 million special charge, with the balance
of the charge included in Cost of sales. As noted previously, $0.7 million of
the special charge was recorded in the third quarter 1998 while the remaining
$21.8 million was recorded in the second quarter 1998. The charge includes the
write-down of certain fixed assets and related intangibles in the
Microelectronic and Metal Systems Groups to their estimated fair market values
in compliance with SFAS No. 121. The Company's current long-term strategic plans
anticipate only modest growth from certain operations and the projected cash
flows were not sufficient to support the carrying value of these assets. Charges
were also taken for the acceleration of depreciation on equipment that will be
taken out of service in the fourth quarter of 1998 as a result of new capital
investment. A reserve for environmental expenses was recorded in support of a
plan to pursue a voluntary remediation program of a former manufacturing site of
a subsidiary under the State of Ohio's Voluntary Action Program. The special
charge is consistent with the Company's long-term goals and objectives and does
not suggest any plans to exit any of the current business units at the present
time.
 
     Interest expense was $0.3 million in the third quarter and $0.8 million in
the nine months of 1998 which is more than the comparable periods in 1997 as a
result of higher debt levels in 1998.
 
     Income before income taxes was $0.1 million in the third quarter 1998
compared to $5.6 million in the third quarter 1997. Excluding the special
charge, third quarter 1998 income before income taxes was $0.8 million. For the
first nine months, the loss before income taxes was $10.3 million in 1998
compared to income of $25.1 million in 1997. Absent the special charge, income
before income taxes was $12.2 million for the first three quarters of 1998.
 
     Income taxes were provided for at a rate of 29.5% of income before income
taxes in third quarter 1998 versus 28.3% in the third quarter 1997. For the
first nine months of 1998, income taxes were applied at a rate of 34.0% of the
pre-tax loss. In 1997, a tax rate of 28.3% was used.
 
     Diluted earnings per share were $0.01 in the third quarter and a loss per
share of $0.42 for the first nine months of 1998. Diluted earnings per share
were $0.24 and $1.10 in the respective periods of 1997.
 
     The Company is subject to litigation involving claims relating to product
liability and other claims relating to alleged beryllium or asbestos exposure
(see "Legal Proceedings"). Management believes that the Company has substantial
defenses and intends to contest such suits vigorously. However, the Company's
results of operations could be materially affected by unfavorable results in one
or more of these cases. Based on information known to the Company, management
believes the outcome of the Company's litigation should not have a material
adverse effect upon the consolidated financial position or cash flow of the
Company.
 
FINANCIAL POSITION
 
     Net cash provided from operations was $10.7 million in the first nine
months of 1998 compared to $19.2 million in the first nine months of 1997. The
main causes for these differences are the lower net income, excluding the
special charge, in the current year and a leveling off of accounts receivable.
The $22.5 million special charge had no effect on the cash flow from operations.
Cash balances at the end of the third quarter 1998 were $3.4 million, versus
$7.2 million at December 31, 1997.
 
                                        9
<PAGE>   11
 
     Inventories increased by $8.9 million during 1998. Purchased raw material
inventories, primarily gold and copper, are usually maintained at fairly low
levels through managed hedge or just-in-time programs. However, the Company's
manufacturing operations are highly vertically integrated and unplanned changes
in sales volumes, as experienced in the second and third quarter 1998, can
result in inventory builds in the short term. Start-up issues with equipment at
the Elmore and Lorain facilities discussed earlier also affected the inventory
build. The majority of the inventory increase is in work-in-process at the
Elmore, Ohio facility.
 
     Progress continued on the $117 million alloy expansion project in Elmore,
Ohio. As previously noted, the casting equipment was placed in service in the
first quarter of this year. The balance of the project is a new strip mill,
which is designed to increase capacity, improve quality and reduce cycle time
and costs and is planned to be substantially completed late in the fourth
quarter of this year. Full integration of all the equipment within the line will
not occur until early next year, and some start-up costs will continue into 1999
as well. The total construction cost estimate remains within the $117 million
budget. This project is being financed in large part by two operating leases.
Lease payments for the building began in December 1997 while the payments for
selected pieces of equipment do not begin until 1999. The lease payments on the
equipment are graduated to increase over time.
 
     Capital expenditures for property, plant and equipment were $29.3 million
in the first nine months of 1998. Major projects include a portion of the alloy
expansion project, the on-going implementation of an enterprise-wide information
system, new plating lines and rolling mills at the Lincoln, Rhode Island
facility and the powder metallurgy operation. The Company also recently began an
expansion of its Buffalo, New York facility in order to enter into the specialty
alloy business.
 
     Consistent with this expansion, late in the second quarter 1998, Williams
Advanced Materials, Inc., a wholly owned subsidiary of the Company, acquired the
assets of Pure Tech Inc. of Carmel, New York for $12.4 million in cash. The
acquisition was accounted for as a purchase.
 
     Total balance sheet debt stood at $83.7 million at the end of the third
quarter 1998, compared to $46.8 million at December 31, 1997. Higher debt levels
were necessary to finance the capital expenditure program, the Pure Tech
acquisition, payment of dividends and stock repurchases. Of the $36.9 million
increase, $10.0 million was borrowed under a multi-currency line with relatively
low interest rates with the balance borrowed under short term domestic lines.
 
     Funds being generated from operations, plus the available borrowing
capacity, are believed to be adequate to support operating requirements, capital
expenditures, remediation projects, dividends and small acquisitions. Excess
cash, if any, is invested in money market or other high quality instruments.
 
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<PAGE>   12
 
PART II OTHER INFORMATION
 
ITEM 1.   LEGAL PROCEEDINGS
 
  (a) Environmental Proceedings.
 
     RECENT DEVELOPMENTS RELATING TO PENDING CLAIMS SINCE THE END OF SECOND
QUARTER 1998. As previously reported in the Company's annual report on Form 10-K
for the year ended December 31, 1997, the Company was identified as one of the
Potentially Responsible Persons (the "PRPs") under the Comprehensive
Environmental Response Compensation and Liability Act ("CERCLA") at the Spectron
Superfund Site in Elkton, Maryland (the "Elkton Site"). The Company reached a
settlement with the U.S. Environmental Protection Agency (the "U.S. EPA")
resolving the Company's liability under the Administrative Orders by Consent
dated August 21, 1989 and October 1, 1991 for the U.S. EPA's initial response
activities at the Elkton Site. The cost of compliance with the terms of these
Orders is approximately $8,480,000, of which the Company's proportionate share
is $20,461. On September 29, 1995, the U.S. EPA sent a "Special Notice for
Negotiations for Remedial Investigation/Feasibility Study" to approximately 700
PRPs, including the Company. The U.S. EPA estimates that the final remedy for
the Elkton Site will cost in the aggregate approximately $45 million. In October
1995, the terms of several proposed de minimis settlement/buyout options
designed to resolve all remaining liability with respect to the Elkton Site were
circulated among a group of PRPs, including the Company. The Company indicated
its willingness to pursue resolution of its liability through a de minimis
settlement/buyout. The Company has received information from the PRP group
negotiating with the U.S. EPA that the terms of such a settlement likely will be
circulated to qualifying PRPs (including the Company) in the third or fourth
quarter of 1998. The U.S. EPA is expected to complete its review shortly and
consummate the settlement before year end. Under the terms of the proposal, the
Company will be eligible to participate in the de minimis settlement.
 
     As previously reported in the Company's annual report on Form 10-K for the
year ended December 31, 1997, on or about September 25, 1992, the Company was
served with a third-party complaint alleging that the Company, along with 159
other third-party defendants, is jointly and severally liable under CERCLA, 42
U.S.C. Sections 9607(a) and 9613(b), for response costs incurred in connection
with the clean-up of hazardous substances in soil and groundwater at the
Douglassville Site (the "Douglassville Site") located in Berks County,
Pennsylvania: UNITED STATES OF AMERICA V. BERKS ASSOCIATES INC., ET AL. V. AAMCO
TRANSMISSIONS, ET AL., Case No. 91-4868, United States District Court for the
Eastern District of Pennsylvania. Third-party complaints adding further parties
were subsequently filed. Prior to the commencement of litigation, the Company
had responded to a request for information from the U.S. EPA by denying that it
arranged to send any substances to the Douglassville Site. Although the Company
has no documents in its own files relating to the shipment of any waste to the
Douglassville Site, documents maintained by third-party plaintiffs suggest that
8,344 gallons of waste oil from the Company may have been taken there. According
to a consultant retained by third-party plaintiffs, approximately 153 million
gallons of waste were sent to the Douglassville Site. The Company denies
liability. The Company participated in court-ordered settlement proceedings,
which resulted in a de minimis settlement offer by the U.S. EPA. In August 1998,
the Company accepted the de minimis settlement offer from the U.S. EPA. The
settlement obligates the Company to pay approximately $15,000 in consideration
for a release of liability from the U.S. EPA's past and future costs to clean up
the Douglassville Site. A reopener clause in the settlement agreement may, if
certain contingencies are met, require the Company to pay an additional $10,000.
 
  (b) Beryllium Exposure Claims.
 
     RECENT DEVELOPMENTS RELATING TO PENDING CLAIMS SINCE THE END OF SECOND
QUARTER 1998. In Ballinger et al. v. Brush Wellman Inc. et al., a product
liability case filed in November 1996 in the United States District Court,
Colorado, 26 plaintiffs who allegedly have chronic beryllium disease ("CBD") and
their spouses, and one representative of a spouse who allegedly died from CBD (a
total of 43 plaintiffs), are claiming recovery based on various legal theories
and seek compensatory and punitive damages of an unspecified amount. None of the
plaintiffs is an employee of the Company. This case was previously reported in
the Company's annual reports on Form 10-K for the years ended December 31, 1997
and 1996. The defendants
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<PAGE>   13
 
filed various motions in response to the complaint, including a motion to
dismiss. Before a ruling on the motion to dismiss, an amended complaint was
filed in September 1997 adding 7 plaintiffs who allegedly have CBD and their
spouses (a total of 14 additional plaintiffs). Various motions were again filed,
including a motion to dismiss. Before a ruling was made on the motion to dismiss
the amended complaint, a second amended complaint was filed in December 1997.
One plaintiff and his spouse moved for dismissal of their claims without
prejudice, which motion was granted. Also, in December 1997, the remaining
plaintiffs agreed to dismiss the second defendant and filed an agreed motion for
dismissal. The Court granted this second agreed motion on February 13, 1998. In
response to the second amended complaint, on January 23, 1998, the Company moved
to dismiss 47 of the 55 plaintiffs based on the statute of limitations and
answered as to the remaining 8 plaintiffs. On June 25, 1998, the Court denied
the Company's motion to dismiss. The Company has now answered the second amended
complaint and each of the parties has filed and served its initial disclosure
statement. The parties have filed an agreed case management order, but the Court
has not yet entered this order. Other than information provided in the
disclosure statement, no discovery may commence until the Court enters the case
management order.
 
     As previously reported in the Company's annual report on Form 10-K for the
year ended December 31, 1997, on December 19, 1997, the Company was named a
defendant, together with Cabot Corporation and NGK Metals Corporation, in a
product liability case filed in the Court of Common Pleas in Philadelphia
County, Pennsylvania: CORVINO ET AL. V. CABOT CORP. ET AL. The Company filed
preliminary objections to the complaint. The Court upheld the Company's
preliminary objections and dismissed the complaint with leave to file an amended
complaint. On August 31, 1998, the plaintiffs filed an amended complaint. Mr.
Corvino alleges that he has developed lung diseases as a result of his exposure
to beryllium either at his place of employment or as a result of discharges of
beryllium into the environment. He seeks recovery under theories of negligence
and strict liability. His wife seeks damages for loss of consortium. Each
plaintiff seeks damages in excess of $50,000, costs of medical monitoring and
punitive damages.
 
     In MORGAN ET AL. V. BRUSH WELLMAN INC. ET AL., a product liability case
originally filed in June 1994 in the United States District Court, Eastern
District of Tennessee, the original complaint named the Company, Cabot
Corporation and NGK Metals Corporation as defendants. This case was previously
reported in the Company's annual reports on Form 10-K for the years ended
December 31, 1997 and prior years. Since the filing of the original complaint,
Ceradyne, Inc., the United States, Lockheed Martin Beryllium Corporation,
Microtechnologies, Inc., Cercom Quality Products, Inc., Maxwell Technologies,
Inc., General Ceramics, Inc. and Eagle-Picher Industries, Inc. have been added
as defendants. In the amended complaint filed effective May 1997 (the third such
amendment), the plaintiffs' aggregate claims against the corporate defendants,
including compensatory and punitive damages, are $44 million. The plaintiffs
allege injury resulting from exposure to beryllium-containing materials other
than as employees of the Company. On or about August 1, 1997, the United States
filed a motion to dismiss the complaint on the grounds that the Court lacked
subject matter jurisdiction. In September 1998, the plaintiffs moved for
additional discovery to respond to this motion, which the government opposed.
Both motions are pending. On or about October 31, 1997, Maxwell Technologies,
Inc. filed a motion for summary judgment. On or about February 4, 1998, counsel
for plaintiffs and for Maxwell Technologies, Inc. submitted an agreed order
granting Maxwell Technologies, Inc.'s motion for summary judgment. This order
was entered by the Court on February 18, 1998. On April 30, 1998, Eagle-Picher
Industries, Inc. was dismissed from the proceedings on the grounds that the
prosecution of the case against it violated an order of the bankruptcy court.
Discovery is continuing.
 
     As previously reported in the Company's annual reports on Form 10-K for the
years ended December 31, 1997 and 1996, Gary Foster and his wife filed a product
liability suit against the Company, Ceradyne, Inc., General Ceramics, Inc.,
Cabot Corporation, NGK Metals Corporation and the United States in the United
States District Court, Eastern District of Tennessee, on or about February 18,
1997: FOSTER ET AL. V. BRUSH WELLMAN INC. ET AL. Eagle-Picher Industries, Inc.
was added as a defendant immediately thereafter. On June 25, 1997, the Court
allowed the plaintiffs to amend their complaint to add Lockheed Martin Beryllium
Corporation, Microtechnologies, Inc., Cercom Quality Products, Inc. and Maxwell
Technologies, Inc. The plaintiffs allege injury resulting from exposure to
beryllium-containing materials other than as employees of the Company. Gary
Foster seeks compensatory damages from each corporate defendant of $5 million.
His spouse seeks compensatory damages from each defendant of $1 million. Both
plaintiffs seek punitive damages from each
 
                                       12
<PAGE>   14
 
defendant of $10 million. On or about August 1, 1997, the United States filed a
motion to dismiss the action on the grounds that the Court lacked subject matter
jurisdiction. This motion is pending. On or about October 31, 1997, Maxwell
Technologies, Inc. filed a motion for summary judgment. On or about February 3,
1998, counsel for plaintiffs and for Maxwell Technologies, Inc. submitted an
agreed order granting Maxwell Technologies, Inc.'s motion for summary judgment.
This order was entered by the Court on February 13, 1998. In March 1998, counsel
for the plaintiffs and for Eagle-Picher Industries, Inc. submitted a final order
of dismissal as to Eagle-Picher Industries, Inc. on the grounds that prosecution
of this action against Eagle-Picher Industries, Inc. violated an order of the
bankruptcy court. This order was entered by the Court on April 7, 1998.
Discovery is continuing.
 
     In another product liability case pending before the United States District
Court, Eastern District of Tennessee, GRANT ET AL. V. BRUSH WELLMAN INC. ET AL.,
the Company is a defendant together with Ceradyne, Inc., General Ceramics, Inc.,
Cabot Corporation, NGK Metals Corporation, Eagle-Picher Industries, Inc.,
Lockheed Martin Beryllium Corporation, Microtechnologies, Inc., Cercom Quality
Products, Inc. and Maxwell Technologies, Inc. The plaintiffs, James Grant and
his wife, originally filed their complaint on or about August 7, 1997, and
allege injury resulting from exposure to beryllium-containing materials other
than as employees of the Company. Mr. Grant seeks compensatory damages of $5
million against each defendant. His wife seeks compensatory damages of $1
million against each defendant, and both plaintiffs seek punitive damages of $10
million against each defendant. This case was previously reported in the
Company's annual report on Form 10-K for the year ended December 31, 1997. On or
about October 31, 1997, Maxwell Technologies, Inc. filed a motion for summary
judgment. On or about February 4, 1998, counsel for plaintiffs and for Maxwell
Technologies, Inc. submitted an agreed order granting the motion for summary
judgment. This order was entered by the Court on February 18, 1998. On or about
April 1998, counsel for plaintiffs and for Eagle-Picher Industries, Inc.
submitted a final order dismissing Eagle-Picher Industries, Inc. as a defendant
on the grounds that prosecution of this action against Eagle-Picher Industries,
Inc. violated a bankruptcy court order. This order was entered by the Court on
April 7, 1998. On April 10, 1998, the plaintiffs filed a motion to amend the
complaint to add the United States as a defendant. This motion was granted by
the Court on July 30, 1998. Discovery is continuing.
 
     CLAIMS INITIATED SINCE THE END OF SECOND QUARTER 1998. On September 18,
1998, the Company and its officers and directors were named defendants in a case
filed in the Superior Court of California, Orange County, California: DOUGLAS
MCLAREN ET AL. V. BRUSH WELLMAN INC. ET AL. The other defendants include Kyocera
International Inc., I.C.M. Inc., TRE Corporation, Aluminum Company of America
and CBL Ceramics, Ltd. McLaren alleges injury resulting from exposure to
beryllium and beryllium-containing materials, other than as an employee of the
Company. The complaint includes claims based on negligence, strict liability,
false representation, intentional tort and breach of express warranty; his wife
claims loss of consortium. The plaintiffs seek compensatory and punitive damages
of an unspecified amount.
 
     CLAIMS CONCLUDED SINCE THE END OF SECOND QUARTER 1998. In two product
liability cases that were pending before the Court of Common Pleas, Montgomery
County, Pennsylvania -- NEIMAN ET AL. V. CABOT CORP. ET AL. (filed November
1990) and ROBBINS ET AL. V. CABOT CORP. ET AL. (filed June 1993) -- the Company
was one of three defendants in each case. The plaintiffs alleged injury
resulting from exposure to beryllium-containing materials, other than as
employees of the Company, and claimed recovery based on various legal theories.
In NEIMAN, the plaintiffs sought damages in excess of $20,000 for personal
injury and in excess of $20,000 for loss of consortium. In Robbins, the
plaintiffs individually sought damages in excess of $50,000 and Mr. Robbins also
sought punitive damages in excess of $50,000. Both cases were previously
reported in the Company's annual reports on Form 10-K for the years ended
December 31, 1997 and prior years. Settlements have been reached in each of
these cases. The settlement of the NEIMAN case was approved by the Court on
September 3, 1998. No such approval is needed for the ROBBINS case. The
Company's portion of the settlement payments in both these cases will be paid by
insurance.
 
  (c) Asbestos Exposure Claims.
 
     Egbert Corp., a subsidiary of the Company (the "Subsidiary"), is a
co-defendant in fifteen pending cases making claims for asbestos-induced illness
allegedly relating to the former operations of the Subsidiary, then known as The
S.K. Wellman Corp. All of these cases have been reported in prior filings with
the S.E.C. In all but
                                       13
<PAGE>   15
 
a small portion of these cases, the Subsidiary is one of a large number of
defendants in each case. The plaintiffs seek compensatory and punitive damages,
in most cases of unspecified sums. Each case has been referred for defense
pursuant to liability insurance coverage and has been accepted for defense
without admission or denial of carrier liability. Two hundred fifty-two similar
cases previously reported have been dismissed or disposed of by pretrial
judgment, one by jury verdict of no liability and fourteen others by settlement
for nominal sums.
 
     The Subsidiary is a party to an agreement with the predecessor owner of its
operating assets, Pneumo Abex Corporation (formerly Abex Corporation), and five
insurers, regarding the handling of these cases. Under the agreement, the
insurers share expenses of defense, and the Subsidiary, Pneumo Abex Corporation
and the insurers share payment of settlements and/or judgments. In certain of
the pending cases, both expenses of defense and payment of settlements and/or
judgments are subject to a limited, separate reimbursement agreement with MLX
Corp., the parent of the company that purchased the Subsidiary's operating
assets in 1986.
 
                                       14
<PAGE>   16
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
  (a) Exhibits
 
<TABLE>
<S>       <C>
          Statement re computation of per share earnings (filed as
    (11)  Exhibit 11 to Part I of this report).
          Financial Data Schedules for the periods ended October 2,
    (27)  1998 and September 26, 1997.
</TABLE>
 
  (b) Reports on Form 8-K
 
  There have been no reports on Form 8-K during the quarter ended October 2,
1998.
 
                                       15
<PAGE>   17
 
                                   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.
 
                                          BRUSH WELLMAN INC.
Dated: November 13, 1998
                                          /s/ Carl Cramer
 
                                          --------------------------------------
                                          Carl Cramer
                                          Vice President Finance and
                                          Chief Financial Officer
 
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