<PAGE>   1
                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 July 3, 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)

             Ohio                                               34-0119320
(State or other jurisdiction of                               (I.R.S. Employer
incorporation or organization)                               Identification No.)

17876 ST. CLAIR AVENUE, CLEVELAND, OHIO                            44110
(Address of principal executive offices)                         (Zip Code)

         Registrant's telephone number, including area code 216-486-4200


     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 August 7, 1998 there were 16,395,610 shares of Common Stock, par
value $1 per share, outstanding.

<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 July 3, 1998 are as follows:

         Consolidated Statements of Income -
                  Six months ended July 3, 1998 and June 27, 1997

         Consolidated Balance Sheets -
                  July 3, 1998 and December 31, 1997

         Consolidated Statements of Cash Flows- 
                  Six months ended July 3, 1998 and June 27, 1997








                                       1
<PAGE>   3
<TABLE>
<CAPTION>
CONSOLIDATED STATEMENTS OF INCOME
(UNAUDITED)

                                                         SECOND QUARTER ENDED                      FIRST HALF ENDED
(Dollars in thousands except                          JULY 3,            JUNE 27,           JULY 3,            JUNE 27,
share and per share amounts)                           1998                1997              1998               1997
------------------------------------------------------------------------------------------------------------------------

<S>                                                <C>                <C>                <C>                <C>
NET SALES                                          $    102,992       $    113,374       $    217,174       $    213,062
  COST OF SALES                                          85,476             83,587            171,629            157,584
                                                   ------------       ------------       ------------       ------------
GROSS MARGIN                                             17,516             29,787             45,545             55,478
  SELLING, ADMINISTRATIVE
  AND GENERAL EXPENSES                                   16,450             17,161             32,783             32,561
  RESEARCH AND DEVELOPMENT
  EXPENSES                                                1,967              1,982              4,172              3,560
  OTHER-NET                                              17,963                 20             18,660               (504)
                                                   ------------       ------------       ------------       ------------
OPERATING PROFIT                                        (18,864)            10,624            (10,070)            19,861
  INTEREST EXPENSE                                          172                 79                408                364
                                                   ------------       ------------       ------------       ------------
INCOME BEFORE INCOME TAXES                              (19,036)            10,545            (10,478)            19,497

  INCOME TAXES                                           (5,952)             3,056             (3,556)             5,518
                                                   ------------       ------------       ------------       ------------

NET INCOME                                         $    (13,084)      $      7,489       $     (6,922)      $     13,979
                                                   ============       ============       ============       ============

PER SHARE OF COMMON STOCK: BASIC                   $      (0.80)      $       0.46       $      (0.42)             $0.86

WEIGHTED AVERAGE NUMBER
  OF COMMON SHARES OUTSTANDING                       16,372,170         16,285,043         16,344,844         16,244,158


PER SHARE OF COMMON STOCK: DILUTED                 $      (0.80)      $       0.46       $      (0.42)             $0.86

WEIGHTED AVERAGE NUMBER
  OF COMMON SHARES OUTSTANDING                       16,372,170         16,582,135         16,344,844         16,477,099


CASH DIVIDENDS PER COMMON SHARE                    $       0.12       $       0.11       $       0.24              $0.22
</TABLE>



SEE NOTES TO CONSOLIDATED FINANCIAL STATEMENTS.





                                       2
<PAGE>   4
<TABLE>
<CAPTION>

CONSOLIDATED BALANCE SHEETS

                                                                 JUL. 3,          DEC. 31,
(DOLLARS IN THOUSANDS)                                            1998             1997
------------------------------------------------------------------------------------------
<S>                                                             <C>               <C>
ASSETS
CURRENT ASSETS
   CASH AND CASH EQUIVALENTS                                    $    747          $  7,170
   ACCOUNTS RECEIVABLE                                            61,593            62,812
   INVENTORIES                                                    95,001            90,714
   PREPAID EXPENSES AND OTHER
     CURRENT ASSETS                                               17,577            18,215
                                                                --------          --------
        TOTAL CURRENT ASSETS                                     174,918           178,911

OTHER ASSETS                                                      38,583            31,319

PROPERTY, PLANT AND EQUIPMENT                                    418,355           463,689
   LESS ALLOWANCES FOR DEPRECIATION,
     DEPLETION AND IMPAIRMENT                                    247,785           290,067
                                                                --------          --------
                                                                 170,570           173,622

                                                                --------          --------
                                                                $384,071          $383,852
                                                                ========          ========

LIABILITIES AND SHAREHOLDERS' EQUITY
CURRENT LIABILITIES
   SHORT-TERM DEBT                                              $ 53,602          $ 28,877
   ACCOUNTS PAYABLE                                                8,979            13,519
   OTHER LIABILITIES AND ACCRUED
     ITEMS                                                        28,822            28,580
   DIVIDENDS PAYABLE                                                                 1,967
   INCOME TAXES                                                     (928)            5,369
                                                                --------          --------
        TOTAL CURRENT LIABILITIES                                 90,475            78,312

OTHER LONG-TERM LIABILITIES                                        6,786             8,200
RETIREMENT AND POST-EMPLOYMENT BENEFITS                           39,389            39,825
LONG-TERM DEBT                                                    17,905            17,905

DEFERRED INCOME TAXES                                              3,927             2,797

SHAREHOLDERS' EQUITY                                             225,589           236,813
                                                                --------          --------
                                                               $ 384,071          $383,852
                                                                ========          ========


</TABLE>

See notes to consolidated financial statements.



                                       3
<PAGE>   5
<TABLE>
<CAPTION>


CONSOLIDATED STATEMENTS OF CASH FLOWS
                                                                                                 FIRST HALF ENDED
                                                                                              JULY 3,          JUNE 27,
(Dollars in thousands)                                                                         1998             1997
-----------------------------------------------------------------------------------------------------------------------

<S>                                                                                            <C>              <C>    
NET INCOME                                                                                     ($6,922)         $13,979
ADJUSTMENTS TO RECONCILE NET INCOME TO NET CASH
  PROVIDED FROM OPERATING ACTIVITIES:
  Depreciation, depletion and amortization                                                      11,852            9,619
  Amortization of mine development                                                               1,937                1
  Decrease (Increase) in accounts receivable                                                       (26)         (20,233)
  Decrease (Increase) in Inventory                                                              (4,784)           3,799
  Decrease (Increase) in prepaid and other current assets                                          246           (1,011)
  Increase (Decrease) in accounts payable and accrued expenses                                  (3,754)           4,948
  Increase (Decrease) in interest and taxes payable                                             (6,230)            (286)
  Increase (Decrease) in deferred income tax                                                     1,130              191
  Increase (Decrease) in other long-term liabilities                                            (1,790)           1,959
  Impairment of fixed assets and related intangibles                                            14,273                  
  Other - net                                                                                      708             (237)
                                                                                                ------          -------
                                 NET CASH PROVIDED FROM OPERATING ACTIVITIES                     6,640           12,729


Cash Flows from Investing Activities:
  Payments for purchase of property, plant and equipment                                       (20,156)         (26,159)
  Payments for mine development                                                                   (258)          (6,932)
  Proceeds from (Payments for) other investments                                               (12,070)             405
                                                                                                ------          -------
                     NET CASH USED IN INVESTING ACTIVITIES                                     (32,484)         (32,686)

Cash Flows from Financing Activities:
  Proceeds from  issuance of short-term debt                                                    27,236           11,367
  Repayment of short-term debt                                                                  (1,652)             (93)
  Proceeds from  issuance of  long-term debt                                                                           
  Repayment of  long-term debt                                                                                     (160)
  Issuance of Common Stock under stock option plans                                              3,433              483
  Purchase of Common Stock for treasury                                                         (3,620)            (508)
  Payments of dividends                                                                         (5,893)          (3,562)
                                                                                                ------          -------
                   NET CASH PROVIDED FROM FINANCING ACTIVITIES                                  19,504            7,527
Effects of Exchange Rate Changes                                                                   (83)          (3,158)
                                                                                                ------          -------
                                       NET CHANGE IN CASH AND CASH EQUIVALENTS                  (6,423)         (15,588)
                              CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                   7,170           31,749
                                                                                                ------          -------
                                    CASH AND CASH EQUIVALENTS AT END OF PERIOD                     747           16,161
                                                                                                ======          =======

</TABLE>

See notes to consolidated financial statements.





                                       4
<PAGE>   6


Notes to Consolidated Financial Statements




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
July 3, 1998 and December 31, 1997 and the results of operations for the three
and six month periods ended July 3, 1998 and June 27, 1997.

<TABLE>
<CAPTION>

NOTE B - INVENTORIES
                                                             JULY 3,                     DEC. 31,
(DOLLARS IN THOUSANDS)                                        1998                        1997
-------------------------------------------------------------------------------------------------

<S>                                                          <C>                          <C>    
Principally average cost:
  Raw materials and supplies                                 $21,231                      $17,331
  In Process                                                  57,595                       58,666
  Finished                                                    37,838                       37,008
                                                             -------                      -------
                                                             116,664                      113,005

Excess of average cost over LIFO
   inventory value                                            21,663                       22,291
                                                             -------                      -------
                                                             $95,001                      $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 second quarter 1998 and 1997, comprehensive income/(loss) amounted to
($13,330,601) and $8,508,685, respectively. Year-to-date 1998 and 1997
comprehensive income/(loss) amounted to ($7,568,532) and $14,016,973,
respectively. The difference between net income/(loss) and comprehensive
income/(loss) is the cumulative translation adjustment for the periods
presented.





                                       5
<PAGE>   7


Notes to Consolidated Financial Statements


NOTE D - SPECIAL CHARGE

In the second quarter 1998, the Company recorded special charges totaling $21.8
million pre-tax and $15.6 million after-tax. The charge resulted primarily from
write-downs of property, plant and equipment, inventory and goodwill, and
increases to environmental reserves. Of the $21.8 million, $4.9 million was
charged to Cost of sales and $16.9 million was charged to Other-net on the
consolidated income statement for the second quarter 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. 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.

Depreciation charges were recorded for equipment that will be taken out of
service with the completion of certain capital projects by December 31, 1998.
This will also result in additional charges of $0.8 million to be recorded in
the second half of 1998. Inventory write-downs and certain provisions were taken
as a result of the reduced 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 by 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 second quarter 1998 were $103.0 million compared to $113.4 million
in the second quarter 1997. The slow down in sales affected both the Metal
System Group and Microelectronic Group profitability in the quarter. In
addition, the Company recorded a special charge of $21.8 million pre-tax that
reduced diluted earnings per share by $0.95 in the second quarter 1998.

Metal Systems Group sales, which were approximately 73% of total sales, declined
in the second quarter 1998 from the second quarter 1997 as higher sales of alloy
bulk products and beryllium metal products were not sufficient to offset lower
sales of alloy strip products and engineered material systems.

Sales of alloy bulk products, primarily copper beryllium alloys in plate, rod,
bar and tube form, improved from the prior year as demand from the aerospace,
mold, oil and gas and undersea communications markets remained strong. Sales of
alloys produced at the Company's new facility in Lorain, Ohio were a minor
contributor to the improvement. Higher beryllium product sales, which service
the aerospace and defense sectors, generated a profit for the third consecutive
quarter after operating at a loss for a number of periods. The majority of both
bulk and beryllium products sales are to domestic customers.

Alloy strip and engineered material system sales decreased in the second quarter
1998 from the second 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 now caused a major
downturn in sales volumes. Prior to the second quarter 1998, the Asian economic
problems had only a minimal impact on the Company's volumes. Automotive is also
a major market for these products and the General Motors strike adversely
affected sales in the second 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 from the Microelectronic Group, which includes precious metal products,
ceramics and thick film circuits, were less in the second quarter 1998 than in
the second quarter 1997. Precious metal reported sales were lower due to a
planned substitution of silver for gold in certain applications. However, the
precious metal value is a straight pass-through to the

                                       7

<PAGE>   9

customer and the underlying unit volumes, value added and profitability are all
higher in the current period compared to the second quarter of last year.
Ceramic sales declined in the second quarter 1998 from the prior year period as
a result of softening demand in the telecommunications market and the General
Motors strike. Yield problems on certain direct bond copper products also
negatively impacted sales and profitability, although some yield improvements
were made late in the quarter. Thick film circuit sales were a minor portion of
total sales and essentially were unchanged from the year ago period.

Year-to-date sales were $217.2 million in 1998 compared to $213.1 million in
1997. Metal System sales increased 7% from last year as sales in the first
quarter 1998 were very strong, compensating for the shortfall in the second
quarter. Microelectronic Group sales were 10% lower in 1998 than in 1997
primarily as a result of the substitution of silver for gold in certain precious
metal applications. The major factors that depressed sales in the second quarter
1998 - weakening demand in the telecommunications and electronics markets, the
Asian economic slow down, the General Motors strike and the stronger U.S. dollar
- have continued into the third quarter 1998.

International sales of all products were $70.1 million in the first six months
of 1998, an 8% 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, were very
strong in the first six months of 1998 while sales in Asia weakened
considerably, especially in the second quarter of 1998.

Gross margin was $17.5 million or 17.0% of sales in the second quarter 1998
compared to $29.8 million or 26.3% of sales in the second quarter 1997.
Included in Cost of sales in the second quarter 1998 was $4.9 million of the
special charge (discussed below). Absent this charge, gross margin would have
been 21.7% of sales in the current quarter. The new casting equipment that was
placed in service in the first quarter has helped to relieve a portion, but not
all, of the capacity constraints that impact bulk and strip alloy products.
However, start-up costs and related manufacturing issues, which are continuing,
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 the alloy expansion project in Elmore, Ohio, the new facility in
Lorain, Ohio 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 second quarter 1998.

For the first six months of 1998 gross margin was $45.5 million or 21.0% of
sales compared to $55.5 million or 26.0% of sales in 1997. The factors affecting
margins in the second quarter apply to the first six months as well.

Selling, administrative and general expenses were $16.5 million or 16.0% of
sales in the second quarter 1998 versus $17.2 million or 15.1% of sales in the
second quarter 1997. For the year, these expenses were $32.8 million or 15.1% of
sales in 1998 and $32.6 million or 15.3% 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
currency effect on expenses is also favorable 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.

                                       8
<PAGE>   10


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 more minor amount 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 December 31, 1998, 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.

Research and development (R&D) expenses were $2.0 million in both the second
quarter 1998 and 1997. R&D expenses of $4.2 million for the first half of 1998
were $0.6 million higher than the comparable period last year. Current major
projects include the development of new alloy system and refinement of casting
processes and technologies.

Included in Other-net in the second quarter 1998 is $16.9 million of the $21.8
million special charge, with the balance of the charge included in Cost of
sales. 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 are 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 second half 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. The total charge is described in Note D to
the Consolidated Financial Statements.

Excluding the special charge, Other-net expense was $1.0 million higher in the
second quarter 1998 than the second quarter 1997. Year-to-date Other-net expense
was $18.7 million in 1998 ($1.8 million without the special charge) compared to
Other-net income of $0.5 million in 1997. Reduced currency hedge gains and a
decline in interest income in 1998 account for the majority of the differences
between periods.

Interest expense was $0.2 million in the second quarter and $0.4 million in the
first half 1998 which is slightly higher than the comparable periods in 1997 as
a result of higher debt levels in 1998. The weighted average interest rate is
lower in 1998 than in 1997. The year-to-date expense is net of capitalized
interest of $0.8 million in 1998 and $0.6 million in 1997.

Income/(loss) before income taxes was $(19.0) million in the second quarter 1998
compared to $10.5 million in the second quarter 1997 and ($10.5) million in the
first six months of 1998 versus $19.5 million in the first six months of 1997.
Excluding the special charge, income before income taxes declined 74% for the
quarter and 42% for the year from the respective



                                       9

<PAGE>   11

periods in 1997. The lower sales and higher manufacturing costs were the main
causes for the reduced earnings.

The income tax benefits were provided for at a rate of 31.3% of the pre-tax loss
for the second quarter and 33.9% for the first six months of 1998 while for 1997
income tax expenses were provided for at 29.0% of pre-tax income for the second
quarter and 28.3% for the first six months. Diluted earnings/(loss) per share
were $(0.80) for the second quarter and $(0.42) for the first half 1998. Diluted
earnings per share were $0.46 and $0.86 for the respective periods in 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 $6.6 million in the first six months of
1998 compared to $12.7 million in the first six months of 1997. The main cause
for this difference is the lower net income, excluding the special charge, in
the current year. The $21.8 million special charge had no effect on the cash
flow from operations in the first six months of 1998. Cash balances at the end
of the second quarter 1998 were $0.8 million, a decrease of $6.4 million since
December 31, 1997.

Inventories increased by $4.3 million during 1998. Purchased raw material
inventories, primarily copper and gold, 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 quarter 1998 can result in
inventory builds in the short term.

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 completed in the second half of the year. The project
remains on schedule and 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.

Capital expenditures for property, plant and equipment were $20.2 million in the
first six months of 1998. Major projects include a portion of the alloy
expansion project, the on-going implementation of an enterprise-wide information
system and new plating lines and rolling mills at the Lincoln, Rhode Island
facility. 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 PureTech Inc. of Carmel, New York for $12.4 million in cash. PureTech
is a manufacturer of specialty alloy and ceramic physical vapor deposition
targets for thin film deposition and its products complement

                                       10


<PAGE>   12

the Company's current and planned offerings. The acquisition was accounted for
as a purchase.

The Company purchased 163,500 shares of its Common Stock at a cost of $3.6
million in the first half of 1998 compared to 23,600 shares at a cost of $0.5
million in the first half of 1997.

Total balance sheet debt stood at $71.5 million at the end of the second
quarter, an increase of $24.7 million since December 31, 1997. Higher debt
levels were necessary to finance the capital expenditure program, the PureTech
acquisition, payment of dividends and stock repurchases. Of the $24.7 million
increase, $6.3 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.


                                      11



<PAGE>   13

PART II   OTHER INFORMATION

ITEM 1.   LEGAL PROCEEDINGS

         (a)      Environmental Proceedings.
                  --------------------------

                  RECENT DEVELOPMENTS RELATING TO PENDING CLAIMS SINCE THE END
OF FIRST QUARTER 1998. As previously reported in the Company's annual report on
Form 10-K for the year ended December 31, 1997, the Company received a complaint
on July 26, 1994 in GLIDDEN COMPANY ET AL. V. AMERICAN COLOR AND CHEMICAL ET
AL., No. 94-C-3970, filed in the United States District Court for the Eastern
District of Pennsylvania. The plaintiffs are five companies that, pursuant to
orders issued by the U.S. Environmental Protection Agency (the "U.S. EPA") under
the Comprehensive, Environmental, Response, Compensation and Liability Act
("CERCLA"), have been spending funds to secure, maintain and conduct an
investigation of the Berks Landfill in Sinking Springs, Pennsylvania (the "Berks
Site"). The plaintiffs are alleged to have disposed of wastes at the Berks Site,
which operated from 1950 through October 1, 1986. The 40 defendants (22 of which
were added in 1997) consist of former owners or operators of the Berks Site and
alleged transporters and/or generators of waste disposed of at the Berks Site.
It is believed that hundreds of other entities disposed of waste at the Berks
Site during its long period of operation. The plaintiffs seek to recover their
past and future costs pursuant to rights of contribution under CERCLA and the
Pennsylvania Hazardous Sites Cleanup Act. Plaintiffs allege that they have spent
approximately $3 million to secure and maintain the Berks Site and to prepare a
remedial investigation/feasibility study and a risk assessment. Discovery is
proceeding pursuant to a case management order, which on April 23, 1998 was
amended to appoint a special master to develop a recommended allocation plan. On
September 30, 1997, the U.S. EPA sent a special notice letter to the Company and
28 other entities, 7 of whom are not parties to the GLIDDEN litigation. The
letter requested reimbursement of the U.S. EPA's past costs (at least $755,959)
and future costs relating to the landfill, and solicited a proposal to conduct
or finance the remedial action selected by the U.S. EPA in its July 1997 Record
of Decision, the present worth cost of which is estimated by the U.S. EPA to be
$6.1 million. The U.S. EPA received no proposal in response to its letter. On
March 31, 1998, the U.S. EPA issued an administrative order to 18 entities, but
not to the Company, directing them to implement the remedy selected in the July
1997 Record of Decision. The Company has been advised by the U.S. EPA that it is
considered by the agency to be a candidate for a de minimis settlement. The
Company's expenses at the Berks Site will be affected by a number of
uncertainties, including the method and extent of remediation, the percentage of
waste disposed of at the Berks Site attributable to the Company relative to that
attributable to other parties, and the financial capabilities of the other
Potentially Responsible Persons (the "PRPs").

                  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 PRPs under CERCLA at the Spectron Superfund Site in Elkton, Maryland (the
"Elkton Site"). The Company reached a settlement with the U.S. EPA resolving the
Company's liability under the Administrative Orders by Consent dated August 21,
1989 and October 1, 1991. 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

                                       12

<PAGE>   14

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.

                  CLAIMS INITIATED SINCE THE END OF FIRST QUARTER 1998. By
letter dated March 6, 1998, the U.S. EPA notified Egbert Corp., a subsidiary of
the Company (the "Subsidiary"), that it was a potentially responsible party
under CERCLA for the remediation of the PCB Treatment Site (the "PCB Treatment
Site") in Kansas City, Kansas, and Kansas City, Missouri. The basis for the U.S.
EPA's letter was the removal from the Subsidiary's facility in 1985 of 10 drums
of oil, 22 drums of solids and three transformers manufactured by High Voltage
Maintenance, which allegedly were shipped, at least in part, to the PCB
Treatment Site. The Subsidiary has requested High Voltage Maintenance to hold it
harmless from any liability arising from this proceeding. To date, the U.S. EPA
has identified approximately 1,800 PRPs for the PCB Treatment Site and has
initiated the process of trying to allocate liability, including consideration
of the issuance of de micromis and/or de minimis settlements to eligible
parties. The Subsidiary's expenses at the PCB Treatment Site will be affected by
a number of uncertainties, including the method and extent of remediation, the
percentage of waste disposed of at the PCB Treatment Site attributable to the
Subsidiary relative to that attributable to other parties, and the financial
capabilities of the other PRPs, including High Voltage Maintenance.

         (b)      Beryllium Exposure Claims.
                  --------------------------

                  RECENT DEVELOPMENTS RELATING TO PENDING CLAIMS SINCE THE END
OF FIRST 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 report on Form 10-K for the year
ended December 31, 1997. The defendants 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.

                  In two other product liability cases 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 is one of three defendants in each case. The
plaintiffs allege injury resulting from exposure to beryllium-containing
materials, other than as employees of the Company, and are claiming

                                       13

<PAGE>   15

recovery based on various legal theories. In NEIMAN, the plaintiffs seek damages
in excess of $20,000 for personal injury and in excess of $20,000 for loss of
consortium. In ROBBINS, the plaintiffs individually seek damages in excess of
$50,000 and Mr. Robbins also seeks 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, but the settlements have not yet been finalized. The
Company's portion of the settlement payments in both these cases will be paid by
insurance.

                  As previously reported in the Company's annual report on Form
10-K for the year ended December 31, 1997, nine Company employees and their
spouses had filed law suits against the Company and certain of its employees in
the Superior Court of Pima County, Arizona: COLE ET AL. V. BRUSH WELLMAN INC. ET
AL.; CRUZ ET AL. V. BRUSH WELLMAN INC. ET AL.; HAYNES-KERN ET AL. V. BRUSH
WELLMAN INC. ET AL.; MATULIN ET AL. V. BRUSH WELLMAN INC. ET AL.; FIMBRES ET AL.
V. BRUSH WELLMAN INC. ET AL.; FLORES ET AL. V. BRUSH WELLMAN INC. ET AL.; KOFIRA
ET AL. V. BRUSH WELLMAN INC. ET AL.; MALDONADO ET AL. V. BRUSH WELLMAN INC. ET
AL.; and STOECKER ET AL. V. BRUSH WELLMAN INC. ET AL. Six of these suits were
instituted on June 29, 1994; one was instituted on December 13, 1994; and two
were instituted on February 28, 1995. The plaintiffs claimed that, during their
employment with the Company, they contracted CBD as a result of exposure to
beryllium and beryllium-containing products. The plaintiffs sought compensatory
and punitive damages of an unspecified amount based on allegations that the
Company intentionally misrepresented the potential danger of exposure to
beryllium and breached an agreement to pay certain benefits should the
plaintiffs contract CBD. These nine cases were dismissed by the trial court
following summary judgments entered in favor of the Company on August 26, 1996.
The plaintiffs appealed the adverse ruling to the Arizona Court of Appeals. On
March 31, 1998, the Court of Appeals filed its decision, affirming in part and
reversing in part the summary judgments. The Court of Appeals held that all of
plaintiffs' common law claims -- breach of contract, breach of implied covenant
of good faith and fair dealing, and fraud -- were barred by the election of
remedy provision in Arizona statutory law. Thus, this portion of the summary
judgments was affirmed. The Court of Appeals further held that the record did
not establish that plaintiffs had waived their claims for willful misconduct by
accepting workers compensation benefits and that a question of fact existed as
to whether that claim was barred by the statute of limitations. The Court made
no ruling on whether there was any merit to any such claim by the plaintiffs.
Plaintiffs and the Company moved for reconsideration of this decision of the
Court of Appeals. Both motions, however, were denied. On July 22 and 24, 1998,
respectively, plaintiffs and the Company filed petitions with the Arizona
Supreme Court for its review of the decision of the Court of Appeals. The
petitions filed with the Arizona Supreme Court are pending.

                  CLAIMS CONCLUDED SINCE THE END OF FIRST QUARTER 1998. In
LINDSTEDT V. NATIONAL BERYLLIUM CORP. ET AL., SPECTRA-PHYSICS, INC. V. BRUSH
WELLMAN INC., a case previously reported in the Company's annual report on Form
10-K for the year ended December 31, 1997, an employee of the Company brought a
suit against a number of defendants, including Spectra Physics, a customer of
the Company, for personal injury resulting from exposure to beryllium-containing
materials. The customer then filed a third-party complaint on December 12, 1996
against the Company in the Superior Court of New Jersey seeking indemnification.
The third-party complaint against the Company was dismissed by the Court in
early 1997. Spectra-Physics has since settled with the plaintiff and has itself
been dismissed from the action. On March 20, 1998, the single remaining
defendant requested, and was granted, permission to identify the Company as a
party for discovery purposes only. The suit against the Company was formally
dismissed on May 4, 1998.

                                       14

<PAGE>   16

                  As previously reported in the Company's annual report on Form
10-K for the year ended December 31, 1997, the Company was a defendant in seven
cases pending before the Court of Common Pleas of Cuyahoga County, Ohio, brought
by current and former employees of the Company and, in most of the cases, their
family members: BERLIN V. BRUSH WELLMAN INC., filed January 24, 1997; KNEPPER ET
AL. V. BRUSH WELLMAN INC., filed January 23, 1997; MIA JOHNSON, EXECUTRIX OF THE
ESTATE OF ETHEL JONES ET AL. V. BRUSH WELLMAN INC., filed January 22, 1997;
JACOBS ET AL. V. BRUSH WELLMAN INC., filed December 31, 1996; STARIN V. BRUSH
WELLMAN INC., filed December 31, 1996; MUSSER ET AL. V. BRUSH WELLMAN INC.,
filed October 25, 1996; and WHITAKER ET AL. V. BRUSH WELLMAN INC., filed August
23, 1996. The complaints in all of these cases alleged that the employees
contracted CBD at the workplace, sought recovery on an intentional tort theory
and, except in the BERLIN and STARIN cases, included claims by family members.
The plaintiffs in these cases sought both compensatory and, except in the
KNEPPER case, punitive damages. All of these cases, except the KNEPPER case,
were consolidated at least for purposes of discovery and pretrial motions. On
October 16, 1997, one of the employee-plaintiffs in the consolidated cases and
his spouse dismissed their complaint without prejudice. On March 20, 1998, the
parties filed an agreed motion to stay and to cancel all scheduled events in
all of the seven cases on the grounds that the parties had negotiated a
settlement and would need time to reduce that settlement to definitive written
agreements. Certain aspects of the proposed settlement were to be submitted for
approval of the probate divisions of the appropriate common pleas courts. The
motion to stay was granted on March 30, 1998. On June 4, 1998, notices of
dismissal were filed in all of the cases, and all of the cases have now been
dismissed with prejudice. The Company's liability insurance carrier has agreed
to contribute a portion of the settlement in all of the foregoing cases, except
the STARIN and BERLIN cases. As described in the Company's Annual Report on
Form 10-K for the year ended December 31, 1997, the Arizona State Compensation
Fund has filed an action in Pima County Superior Court, Arizona, seeking a
declaratory judgment that the Fund is not required to defend or indemnify the
Company against claims made in the WHITAKER case: STATE COMPENSATION FUND V.
BRUSH WELLMAN INC., filed December 11, 1996. The parties have agreed to stay
further proceedings in the case for a mutually agreed period of time.

         (c)      Asbestos Exposure Claims.
                  -------------------------

                  The Subsidiary is a co-defendant in seventeen 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 but one of these
cases have been reported in prior filings with the S.E.C. In all but 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 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.


                                       15

<PAGE>   17

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

         (a) The Company's Annual Meeting of Shareholders for 1998 was held on
             May 5, 1998.

         (b) At the Annual Meeting, three directors were elected to serve for a
             term of three years by the following vote:
<TABLE>
<CAPTION>

                                                   Shares Voted          Shares Voted          Shares Voted
                                                      "For"               "Against"            "Abstaining"
                                                 -----------------     -----------------     -----------------
                   <S>                              <C>                      <C>                 <C>
                   Joseph P. Keithley               13,500,149               -0-                 871,509
                   William R. Robertson             13,527,256               -0-                 844,402
                   John Sherwin, Jr.                13,527,131               -0-                 844,527
</TABLE>

             The following directors' continued their term of office after
             the meeting: Gordon D. Harnett, William P. Madar, Robert M.
             McInnes, Albert C. Bersticker, Dr. Charles F. Brush, III, and
             David L. Burner.

         (c)     (1) An amendment to the Brush Wellman Inc. 1995 Stock Incentive
                 Plan was approved by the following vote:

<TABLE>
<CAPTION>
                                                   Shares Voted          Shares Voted         Shares Voted
                                                      "For"               "Against"           "Abstaining"
                                                 -----------------     -----------------    ------------------
                   <S>                              <C>                   <C>                    <C>
                                                    13,050,486            1,212,400              108,772
</TABLE>

             (2) Adoption of the Brush Wellman Inc. 1997 Incentive Plan for
                 Non-Employee Directors was approved by the following vote:
<TABLE>
<CAPTION>

                                                   Shares Voted          Shares Voted         Shares Voted
                                                      "For"               "Against"           "Abstaining"
                                                 -----------------     -----------------    ------------------
                   <S>                              <C>                   <C>                    <C>
                                                    12,664,941            1,551,086              155,631
</TABLE>

              (3) The selection of Ernst & Young LLP as independent auditors for
                  1998 was ratified and approved by the following vote:
<TABLE>
<CAPTION>

                                                   Shares Voted          Shares Voted         Shares Voted
                                                      "For"               "Against"           "Abstaining"
                                                 -----------------     -----------------    ------------------
                   <S>                              <C>                   <C>                    <C>
                                                    14,231,450              59,705                80,503
</TABLE>

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

         (a) Exhibits

             (10a)* Form of Employment Agreement entered into by the Company and
                    Mr. William R. Seelbach dated June 29, 1998.

             (10b)* Employment Arrangement between the Company and Mr. William
                    R. Seelbach dated June 3, 1998.

             (10c)* Addendum to Employment Arrangement between the Company and
                    Mr. William R. Seelbach dated June 24, 1998.    

             (10d)  Form of Indemnification Agreement entered into by the
                    Company and Mr. William R. Seelbach dated June 29, 1998.

             (10e)* Key Employee Share Option Plan (filed on Form S-8 on May 5,
                    1998), incorporated herein by reference.  
                 
             (11)   Statement re computation of per share earnings (filed as
                    Exhibit 11 to Part I of this report).

             (27)   Financial Data Schedules for the periods ended July 3, 1998
                    and June 27, 1997.

         (b) Reports on Form 8-K

             The Company filed a report on Form 8-K on July 27, 1998 which
             included a copy of a press release containing the Company's
             financial results for the quarter ended July 3, 1998.

-------
* Reflects management contract or other compensatory arrangement required to be
  filed as an Exhibit pursuant to Item 6(a) of this report.


                                       16
<PAGE>   18

                                   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:   August 17, 1998



                                                     /s/Carl Cramer
                                                     ---------------------------
                                                     Carl Cramer
                                                     Vice President Finance and
                                                     Chief Financial Officer

                                       17