<PAGE>   1

 
================================================================================
 
                       SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D. C. 20549
 
                                   FORM 10-Q
                   QUARTERLY REPORT UNDER SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
 
(Mark One)
 
[ X ]  QUARTERLY REPORT PURSUANT TO SECTION 13 or 15(d) OF THE SECURITIES
       EXCHANGE ACT OF 1934
 
FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1997
 
                                       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 1-10319
 
                              RMI TITANIUM COMPANY
             (Exact name of registrant as specified in its charter)
 
                 OHIO                                 31-0875005
   (State or other jurisdiction of                 (I.R.S. Employer
    incorporation or organization)                Identification No.)
 
                     1000 WARREN AVENUE, NILES, OHIO 44446
                    (Address of principal executive offices)
 
                                 (330) 544-7700
              (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 __
 
     At November 1, 1997, 20,434,946 shares of common stock of the registrant
were outstanding.
 
================================================================================
<PAGE>   2
 
                              RMI TITANIUM COMPANY
 
                                   FORM 10-Q
                        QUARTER ENDED SEPTEMBER 30, 1997
 
                                     INDEX
 
<TABLE>
<CAPTION>
                                                                                         PAGE
                                                                                         ----
<S>                                                                                      <C>
PART I--FINANCIAL INFORMATION
Item 1. Consolidated Financial Statements:
     Introduction to Consolidated Financial Statements................................     2
     Consolidated Statement of Income.................................................     3
     Consolidated Balance Sheet.......................................................     4
     Consolidated Statement of Cash Flows.............................................     5
     Consolidated Statement of Shareholders' Equity...................................     6
     Selected Notes to Consolidated Financial Statements..............................     7
Item 2. Management's Discussion and Analysis of Results of Operations and Financial
        Condition.....................................................................    10
PART II--OTHER INFORMATION
Item 6. Exhibits and Reports on Form 8-K..............................................    21
Signatures............................................................................    22
</TABLE>
<PAGE>   3
 
                         PART I--FINANCIAL INFORMATION
 
ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS
 
               INTRODUCTION TO CONSOLIDATED FINANCIAL STATEMENTS
 
     The consolidated financial statements included herein have been prepared by
RMI Titanium Company (the "Company"), without audit, pursuant to the rules and
regulations of the Securities and Exchange Commission. The financial information
presented reflects all adjustments, consisting only of normal recurring
adjustments, which are, in the opinion of management, necessary for a fair
statement of the results for the interim periods presented. The results for the
interim periods are not necessarily indicative of the results to be expected for
the year.
 
                                        2
<PAGE>   4

 
                              RMI TITANIUM COMPANY
 
                      CONSOLIDATED STATEMENT OF OPERATIONS
                                  (UNAUDITED)
 
                             (DOLLARS IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                  QUARTER ENDED              NINE MONTHS ENDED
                                                  SEPTEMBER 30                 SEPTEMBER 30
                                              ---------------------       -----------------------
                                               1997          1996           1997           1996
                                              -------       -------       --------       --------
<S>                                           <C>           <C>           <C>            <C>
Sales....................................     $86,438       $64,479       $235,180       $177,386
Operating costs:
Cost of sales............................      66,624        52,854        182,869        146,134
Selling, general and administrative
  expenses...............................       3,718         2,575          9,249          7,294
Research, technical and product
  development expenses...................         883           390          2,285          1,456
                                              -------       -------       --------       --------
     Total operating costs...............      71,225        55,819        194,403        154,884
Operating income.........................      15,213         8,660         40,777         22,502
Other income-net.........................         275           184            701            244
Interest expense.........................         (74)         (142)          (133)        (1,978)
                                              -------       -------       --------       --------
Income before income taxes...............      15,414         8,702         41,345         20,768
Provision (credit) for income taxes
  (Note 3)...............................      (7,128)       (2,136)        (4,205)          (607)
                                              -------       -------       --------       --------
Net income...............................     $22,542       $10,838       $ 45,550       $ 21,375
                                              =======       =======       ========       ========
Net income per common share..............     $  1.10       $  0.54       $   2.23       $   1.19
                                              =======       =======       ========       ========
       Weighted average shares
          outstanding....................  20,472,439    20,133,416     20,387,072     17,930,408
                                           ==========    ==========     ==========     ========== 
</TABLE>
 
  The accompanying notes are an integral part of these Consolidated Financial
                                  Statements.
 
                                        3
<PAGE>   5
 
                              RMI TITANIUM COMPANY
 
                           CONSOLIDATED BALANCE SHEET
                             (DOLLARS IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                                     (UNAUDITED)
                                                                     SEPTEMBER 30      DECEMBER 31
                                                                         1997              1996
                                                                     ------------      ------------
<S>                                                                  <C>               <C>
ASSETS
Current assets:
  Cash and cash equivalents.......................................     $ 19,644          $  5,944
  Receivables--less allowance for doubtful accounts of
  $1,158 and $979.................................................       70,928            57,702
  Inventories.....................................................      107,384            92,616
  Deferred tax asset..............................................        8,554             2,733
  Other current assets............................................        6,439             4,205
                                                                     ------------      ------------
     Total current assets.........................................      212,949           163,200
  Property, plant and equipment, net of accumulated
     depreciation.................................................       40,840            37,855
  Noncurrent deferred tax asset...................................        2,851             4,467
  Other noncurrent assets.........................................       10,362            10,358
                                                                     ------------      ------------
     Total assets.................................................     $267,002          $215,880
                                                                     ==========        ==========
LIABILITIES AND SHAREHOLDERS' EQUITY
Current liabilities:
  Current portion of long-term debt...............................     $    120          $    120
  Accounts payable................................................       18,617            15,288
  Accrued wages and other employee costs..........................        7,846             6,299
  Other accrued liabilities.......................................       11,297             9,357
                                                                     ------------      ------------
     Total current liabilities....................................       37,880            31,064
Long-term debt....................................................        1,249             3,600
Accrued postretirement benefit cost...............................       19,442            19,442
Noncurrent pension liabilities....................................        1,028             1,028
Other noncurrent liabilities......................................        2,010             2,010
                                                                     ------------      ------------
     Total liabilities............................................       61,609            57,144
                                                                     ------------      ------------
Contingencies (Note 4)
Shareholders' equity:
  Preferred Stock, no par value; 5,000,000 shares authorized; no
     shares outstanding...........................................           --                --
  Common Stock, $0.01 par value, 30,000,000 shares authorized;
     21,005,907 and 20,858,748 shares issued......................          209               208
  Additional paid-in capital......................................      236,830           234,958
  Accumulated deficit.............................................      (26,217)          (71,767)
  Deferred compensation...........................................       (1,176)             (557)
  Excess minimum pension liability................................       (1,028)           (1,028)
  Treasury Common Stock at cost 573,961 and 568,198 shares........       (3,225)           (3,078)
                                                                     ------------      ------------
Total shareholders' equity........................................      205,393           158,736
                                                                     ------------      ------------
     Total liabilities and shareholders' equity...................     $267,002          $215,880
                                                                     ==========        ==========
</TABLE>
 
  The accompanying notes are an integral part of these Consolidated Financial
                                  Statements.
 
                                        4
<PAGE>   6
 
                              RMI TITANIUM COMPANY
 
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                                  (UNAUDITED)
 
                             (DOLLARS IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                                           NINE MONTHS ENDED
                                                                             SEPTEMBER 30
                                                                         ---------------------
                                                                           1997         1996
                                                                         --------     --------
<S>                                                                      <C>          <C>
CASH PROVIDED FROM (USED IN) OPERATIONS:
Net income............................................................   $ 45,550     $ 21,375
Adjustment for items not affecting funds from operations:
  Depreciation........................................................      3,791        3,711
  Deferred taxes......................................................     (4,205)        (607)
  Other-net...........................................................        393          516
                                                                         --------     --------
                                                                           45,529       24,995
                                                                         --------     --------
CHANGES IN ASSETS AND LIABILITIES (EXCLUDING CASH):
Receivables...........................................................    (10,433)     (14,278)
Inventories...........................................................    (12,538)     (20,584)
Accounts payable......................................................        639       (2,767)
Other current liabilities.............................................      3,046       (1,963)
Noncurrent pension liabilities........................................         --      (16,100)
Other assets..........................................................     (2,509)      (1,074)
                                                                         --------     --------
                                                                          (21,795)     (47,306)
                                                                         --------     --------
     Cash from (used in) operating activities.........................     23,734      (22,311)
                                                                         --------     --------
CASH FLOWS FROM INVESTING ACTIVITIES:
  Investment in Galt Alloys, Inc. net of cash acquired................     (2,605)          --
  Capital expenditures................................................     (4,444)      (2,392)
                                                                         --------     --------
     Cash used in investing activities................................     (7,049)      (2,392)
                                                                         --------     --------
CASH FLOWS (USED IN) FROM FINANCING ACTIVITIES:
  Net proceeds from issuance of Common Stock..........................      1,041       82,307
  Borrowings under credit agreements..................................         --        5,900
  Debt repayments.....................................................     (3,879)     (63,290)
  Treasury Common Stock purchased.....................................       (147)          --
                                                                         --------     --------
  Cash (used in) from financing activities............................     (2,985)      24,917
                                                                         --------     --------
INCREASE IN CASH AND CASH EQUIVALENTS.................................     13,700          214
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD......................   $  5,944     $    509
                                                                         --------     --------
CASH AND CASH EQUIVALENTS AT END OF PERIOD............................   $ 19,644     $    723
                                                                         ========     ========
SUPPLEMENTAL CASH FLOW INFORMATION:
  Cash paid for
     Interest (net of amounts capitalized)............................   $     65     $  2,466
     Income taxes.....................................................   $    879     $    211
  Noncash financing activities
     Issuance of restricted stock.....................................   $    832     $    682
</TABLE>
 
  The accompanying notes are an integral part of these Consolidated Financial
                                  Statements.
 
                                        5
<PAGE>   7
 
                              RMI TITANIUM COMPANY
 
                 CONSOLIDATED STATEMENT OF SHAREHOLDERS' EQUITY
                                  (UNAUDITED)
 
                             (DOLLARS IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                                                                                    EXCESS
                                                                                                                   MINIMUM
                                                                             ADDT'L.     RETAINED     TREASURY     PENSION
                                      SHARES       COMMON      DEFERRED      PAID-IN     EARNINGS      COMMON     LIABILITY
                                    OUTSTANDING    STOCK     COMPENSATION    CAPITAL     (DEFICIT)     STOCK      ADJUSTMENT
                                    -----------    ------    ------------    --------    ---------    --------    ----------
<S>                                 <C>            <C>       <C>             <C>         <C>          <C>         <C>
Balance at December 31, 1995.....   15,339,893      $159       $     --      $151,715    $(103,526)   $(3,078)     $ (8,381)
Shares issued for Directors'
  Compensation...................        2,585        --             --            56           --         --            --
Shares issued for Restricted
  Stock Award Plans..............       51,000        --           (682)          682           --         --            --
Compensation expense
  recognized.....................           --        --            125            --           --         --            --
Shares issued as a result of
  Common Stock Offering 
  (Note 4).......................    4,600,000        46             --        80,347           --         --            --
Shares issued from exercise of
  employee stock options.........      297,072         3             --         2,158           --         --            --
Net income.......................           --        --             --            --       31,759         --            --
Excess minimum pension
  liability......................           --        --             --            --           --         --         7,353
                                    -----------    ------    ------------    --------    ---------    --------    ----------
Balance at December 31, 1996.....   20,290,550      $208       $   (557)     $234,958    $ (71,767)   $(3,078)     $ (1,028)
Shares issued for Restricted
  Stock Award Plans..............       32,550        --           (832)          832           --         --            --
Compensation expense
  recognized.....................           --        --            213            --           --         --            --
Shares issued from exercise of
  employee stock options.........      114,609         1             --         1,040           --         --            --
Treasury Common Stock purchased
  at cost........................       (5,763)       --             --            --           --       (147)           --
Net income.......................           --        --             --            --       45,550         --            --
                                    -----------    ------    ------------    --------    ---------    --------    ----------
Balance at September 30, 1997....   20,431,946      $209       $ (1,176)     $236,830    $ (26,217)   $(3,225)     $ (1,028)
                                    ==========     =======   ============    ========    =========    =======     =========
</TABLE>
 
  The accompanying notes are an integral part of these Consolidated Financial
                                  Statements.
 
                                        6
<PAGE>   8
 
                              RMI TITANIUM COMPANY
 
              SELECTED NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                  (UNAUDITED)
 
NOTE 1--GENERAL
 
     The consolidated financial statements include the accounts of RMI Titanium
Company and its majority owned subsidiaries. All significant intercompany
transactions are eliminated. The Company's operations are conducted in one
business segment, the production and marketing of titanium metal and related
products.
 
     On July 3, 1997, the Company acquired 90% of the common stock of Galt
Alloys, Inc., a manufacturer of ferrotitanium and a producer and worldwide
distributor of specialty alloys to ferrous and nonferrous customers. RMI's
investment in Galt amounts to an initial cash investment of $3 million and an
agreement to invest up to an additional $17 million to finance a major expansion
program at Galt, which is expected to be completed in the next 18 to 24 months.
 
NOTE 2--ORGANIZATION
 
     The Company is a successor to entities that have been operating in the
titanium industry since 1958. In 1990, USX Corporation ("USX") and Quantum
Chemical Corporation ("Quantum") transferred their entire ownership interest in
the Company's immediate predecessor, RMI Company, an Ohio general partnership,
to the Company in exchange for shares of the Company's Common Stock (the
"Reorganization"). Quantum then sold its shares to the public. USX retained
ownership of its shares. At June 30, 1997 approximately 27% of the outstanding
common stock was owned by USX.
 
     In November, 1996, USX Corporation completed a public offering of its notes
exchangeable February, 2000, for 5,483,600 shares of RMI Common Stock, owned by
USX (or for an equivalent amount of cash at USX's option). Such shares represent
all of the RMI Common Stock owned by USX.
 
NOTE 3--INCOME TAXES
 
     In the three and nine month periods ended September 30, 1997 the Company
recorded an income tax benefit of $7.1 million and $4.2 million, respectively.
These amounts are comprised of an income tax provision against pretax income for
the nine-month period of $4.5 million and the three-month period of $1.6 million
and an income tax benefit of $8.7 million for both periods, resulting from an
adjustment to the deferred tax asset valuation allowance due to changes in the
Company's expectations about the ultimate realization of its deferred tax assets
in years after 1997. Both the three months and nine months ended September 30,
1996 include a $2.6 million tax benefit. Excluding the $8.7 million valuation
allowance adjustment, the effective tax rate for the three months and the nine
months ended September 30, 1997 was approximately 10.1 percent and 10.8 percent,
respectively. The difference between the statutory federal tax rate of 35
percent and the effective tax rate is principally due to adjustments to the
deferred tax asset valuation allowance which existed at December 31, 1996 as it
related to expected 1997 results. The Company currently expects improved
profitability in 1997 compared to the expectations inherent in the December 31,
1996 deferred tax asset. The amount of current taxes expected to be paid in 1997
will consist primarily of alternative minimum taxes.
 
     Statement of Financial Accounting Standards No. 109 (SFAS No. 109),
"Accounting for Income Taxes," requires a valuation allowance when it is "more
likely than not" that some portion or all of the deferred tax assets will not be
realized. It further states that "forming a conclusion that a valuation
allowance is not needed is difficult when there is negative evidence such as
cumulative losses in recent years." The ultimate realization of this deferred
income tax asset depends upon the Company's ability to generate sufficient
taxable income prior to the expiration of its loss carryforwards. The Company
has evaluated the available evidence supporting the realization of future
taxable income and, based upon that evaluation, believes it is more likely than
not at this time that a portion of its deferred tax assets will be realized. The
remaining valuation allowance was retained in light of the requirement in SFAS
No. 109 to give weight to objective evidence such as recent losses and the
historical titanium industry business cycle.
 
                                        7
<PAGE>   9
 
     When preparing future periods' interim and annual financial statements, the
Company will periodically evaluate its strategic and business plans, in light of
evolving business conditions, and the valuation allowance will be adjusted for
changes in future income expectations resulting from that process.
 
NOTE 4--CONTINGENCIES
 
     In the ordinary course of business, the Company is subject to pervasive
environmental laws and regulations concerning the production, handling, storage,
transportation, emission, and disposal of waste materials and is also subject to
other federal and state laws and regulations regarding health and safety
matters. These laws and regulations are constantly evolving, and it is not
currently possible to predict accurately the ultimate effect these laws and
regulations will have on the Company in the future.
 
     The Company is involved in investigative or cleanup projects under federal
or state environmental laws at a number of waste disposal sites, including the
Fields Brook Superfund Site. Given the status of the proceedings with respect to
these sites, ultimate investigative and remediation costs cannot presently be
accurately predicted, but could, in the aggregate, be material. Based on the
information available regarding the current ranges of estimated remediation
costs at currently active sites, and what the Company believes will be its
ultimate share of such costs, provisions for environmental-related costs have
been recorded. These provisions are in addition to amounts which have previously
been accrued for the Company's share of environmental study costs.
 
     With regard to the Fields Brook Superfund Site, the Company, together with
31 other companies, has been identified by the EPA as a potentially responsible
party ("PRP") with respect to a superfund site defined as the Fields Brook
Watershed in Ashtabula, Ohio, which includes the Company's now closed Ashtabula
facilities. The EPA's 1986 estimate of the cost of remediation of the Fields
Brook operable sediment unit was $48 million. However, recent studies show the
volume of sediment to be substantially lower than projected in 1986. These
studies, together with improved remediation technology and redefined cleanup
standards have resulted in a more recent estimate of the remediation cost of
approximately $25 million. The actual cost of remediation may vary from the
estimate depending upon any number of factors.
 
     The EPA, in March 1989, ordered 22 of the PRPs to conduct a design phase
study for the sediment operable unit and a source control study, which studies
are currently estimated to cost $22 million. The Company, working cooperatively
with fourteen others in accordance with two separate agreements, is complying
with the order. The Company has accrued and has been paying its portion of the
cost of complying with the EPA's order, which includes the studies. It is
anticipated that the studies will be completed no earlier than late 1997. Actual
cleanup would not commence prior to 1998. The Company's share of the study costs
has been established at 9.95%. In June, 1995, the Company and twelve others
entered into a Phase 2 (actual cleanup) allocation agreement which assigns 9.44%
of the cost to the Company. However, the actual percentage may be more or less
based on contributions from other parties which are not currently participating
in the Phase 2 allocation agreement.
 
     At September 30, 1997, the amount accrued for future environmentalrelated
costs was $2.6 million. Based on available information, RMI believes its share
of potential environmental-related costs, before expected contributions from
third parties, is in a range from $3.9 million to $6.5 million, in the
aggregate. The amount accrued is net of expected contributions from third
parties (which does not include any amounts from insurers) of approximately $2.1
million, which the Company believes are probable. The Company has been receiving
contributions from such third parties for a number of years as partial
reimbursement for costs incurred by the Company. As these proceedings continue
toward final resolution, amounts in excess of those already provided may be
necessary to discharge the Company from its obligations for these projects.
 
     The Company is also the subject of, or a party to, a number of other
pending or threatened legal actions involving a variety of matters.
 
     The ultimate resolution of these foregoing contingencies could,
individually or in the aggregate, be material to the consolidated financial
statements. However, management believes that the Company will
 
                                        8
<PAGE>   10
 
remain a viable and competitive enterprise even though it is possible that these
matters could be resolved unfavorably.
 
NOTE 5--INVENTORIES:
 
<TABLE>
<CAPTION>
                                                             (DOLLARS IN THOUSANDS)
                                                      SEPTEMBER 30,
                                                           1997
                                                       (UNAUDITED)       DECEMBER 31, 1996
                                                      --------------     -----------------
    <S>                                               <C>                <C>
    Raw material and supplies......................      $ 51,745            $  33,126
    Work-in-process and finished goods.............        84,475               88,326
    Adjustments to LIFO values.....................       (28,836)             (28,836)
                                                         --------             --------
                                                         $107,384            $  92,616
                                                         ========             ========
</TABLE>
 
     Inventories are valued at cost as determined by the last-in, first-out
(LIFO) method which, in the aggregate, is lower than market. Inventory costs
generally include materials, labor costs and manufacturing overhead (including
depreciation).
 
     Included in work-in-process are costs relating to certain long-term
contracts. Such costs, net of amounts recognized to date, were $3.0 million at
September 30, 1997 and $0.8 million at December 31, 1996.
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
FINANCIAL CONDITION
 
     The following discussion should be read in connection with the information
contained in the Consolidated Financial Statements and Selected Notes to
Consolidated Financial Statements. The following information contains
"forward-looking statements" within the meaning of the Private Securities
Litigation Reform Act of 1995, and are subject to the safe harbor created by
that Act. Such forwardlooking statements include, without limitation, statements
regarding the future availability and prices of raw materials, the
competitiveness of the titanium industry, demand for the Company's products, the
historic cyclicality of the titanium and aerospace industries, the Company's
order backlog and the conversion of that backlog into revenue and other
statements contained herein that are not historical facts. Because such
forward-looking statements involve risks and uncertainties, there are important
factors that could cause actual results to differ materially from those
expressed or implied by such forward-looking statements. These and other risk
factors are set forth below in the "Outlook" section, as well as having been
described in the Company's other filings with the Securities and Exchange
Commission ("SEC") over the last 12 months, copies of which are available from
the SEC or may be obtained upon request from the Company.
 
THREE MONTHS ENDED SEPTEMBER 30, 1997 COMPARED TO THREE MONTHS ENDED SEPTEMBER
30, 1996
 
NET SALES
 
     Net sales amounted to $86.4 million for the three months ended September
30, 1997, compared to net sales of $64.5 million in the corresponding 1996
period, an increase of $21.9 million or 34%. This sales increase is due
primarily to increased average selling prices for titanium mill products, and a
shift in product mix to more value added products such as sheet and plate and
away from commodity type products such as billet and bloom used in the golf club
markets. Shipments of titanium mill products in the third quarter of 1997
amounted to 4.7 million pounds compared to 4.6 million pounds in the third
quarter of 1996. Average selling prices on mill products in the third quarter of
1997 increased by approximately 19% to $14.59 per pound from $12.26 per pound in
the third quarter of 1996. Pricing on incoming orders for titanium mill products
continues to show improvement.
 
GROSS PROFIT
 
     Gross profit amounted to $19.8 million, or 22.9% of sales for the quarter
ended September 30, 1997 compared to a gross profit of $11.6 million or 18.0% of
sales for the comparable 1996 period. This improvement results primarily from
increased profit margins on titanium mill products resulting from a more
favorable product mix and higher average selling prices.
 
                                        9
<PAGE>   11
 
SELLING, GENERAL AND ADMINISTRATIVE EXPENSES
 
     Selling, general and administrative expenses amounted to $3.7 million for
the quarter ended September 30, 1997 compared to $2.6 million for the same
quarter in 1996. Research, technical and product development expenses amounted
to $0.9 million in the third quarter of 1997 compared to $0.4 million in the
third quarter of 1996. The increase in selling, general and administrative
expenses is due primarily to increased levels of business activity and the
inclusion of Galt Alloys, Inc. Selling, general and administrative expenses
together with research, technical and product development expenses amounted to
approximately 5.3% of sales in the third quarter of 1997 compared to 4.6% of
sales in the comparable 1996 period.
 
OPERATING INCOME
 
     Operating income for the three months ended September 30, 1997 amounted to
$15.2 million, or 17.6% of sales compared to $8.7 million or 13.4% of sales in
the same period of 1996. This improvement results primarily from significant
increases in profit margins on mill products.
 
INTEREST EXPENSE
 
     Because of decreased average borrowing levels, interest expense decreased
to $0.07 million in the third quarter of 1997 from $0.1 million in the third
quarter of 1996. For further information on borrowings see "Liquidity and
Capital Resources."
 
INCOME TAXES
 
     In the third quarter of 1997, the Company recorded an income tax benefit of
$7.1 million compared to a benefit of $2.1 million in the third quarter of 1996.
Included in the three months ended September 30, 1997 is an $8.7 million benefit
resulting from an adjustment in the deferred tax valuation allowance due to
changes in the Company's expectations about the ultimate realization of its
deferred tax assets in years after 1997. The three months ended September 30,
1996 includes a similar benefit of $2.6 million. Exclusive of these adjustments,
the effective federal tax rate for the third quarter of 1997 and 1996 was
approximately 10.1% and 10.8%, respectively. The difference between the
statutory tax rate of 35% and the effective tax rate for the third quarter of
1997 and 1996 is principally due to an adjustment of approximately $3.8 million
and $1.5 million, respectively, to the deferred tax asset valuation allowance.
The Company currently expects improved profitability in 1997 as a result of
increased sales, product pricing and gross margins, when compared to the
expectation inherent in the December 31, 1996 valuation allowance. Accordingly,
the valuation allowance was adjusted for the difference between such revised
future income expectations and those inherent in the valuation allowance at
December 31, 1996. The amount of current taxes expected to be paid in 1997 will
approximate $1.0 million. For further information on income taxes, see "Income
Tax Considerations" and "SFAS No. 109 Effects" below.
 
OTHER INCOME
 
     Other income for the third quarter of 1997 amounted to $0.3 million
compared to $0.2 million in the same quarter of 1996.
 
NET INCOME
 
     Net income for the quarter ended September 30, 1997 amounted to $22.5
million or 26% of sales compared to $10.8 million, or 16.8% of sales in the
comparable 1996 period.
 
NINE MONTHS ENDED SEPTEMBER 30, 1997 COMPARED TO NINE MONTHS ENDED SEPTEMBER 30,
1996
 
NET SALES
 
     Net sales for the nine months ended September 30, 1997 increased to $235.2
from $177.4 million in the first nine months of 1996, an increase of $57.8
million, or 32.5%. This increase results primarily from higher
 
                                       10
<PAGE>   12
 
average selling prices for titanium mill products, increased mill product
shipments and an improved product mix. Mill products shipments for the first
nine months of 1997 amounted to 14.2 million pounds compared to 13.4 million
pounds in the comparable period of 1996. Average realized transaction prices
increased to $14.12 per pound in the first nine months of 1997 compared to
$11.71 per pound in 1996. Both demand and pricing for titanium mill products
remain strong.
 
GROSS PROFIT
 
     Gross profit for the nine months ended September 30, 1997 amounted to $52.3
million, or 22.2% of sales compared to $31.3 million, or 17.6% of sales in the
first nine months of 1996. This increase results primarily from increased
selling prices for titanium mill products and increased volume.
 
SELLING, GENERAL AND ADMINISTRATIVE EXPENSES
 
     Selling, general and administrative expenses amounted to $9.2 million for
the first nine months of 1997 compared to $7.3 million for the comparable period
in 1996. The increase in selling, general and administrative expenses results
primarily from increased levels of business activity as well as the inclusion of
Galt Alloys, Inc. Research, technical and product development expenses amounted
to $2.3 million, and $1.5 million in the nine month periods ended September 30,
1997 and 1996, respectively. Selling, general and administrative expenses
together with research, technical and product development expenses for the first
nine months of 1997 and 1996 amounted to 4.9% of sales, respectively.
 
OPERATING INCOME
 
     Operating income for the nine months ended September 30, 1997 amounted to
$40.8 million, or 17.3% of sales compared to $22.5 million, or 12.7% of sales in
the same period of 1996. This improvement results primarily from increases in
average realized transaction prices and mill product shipments, as well as an
improvement in product mix.
 
INTEREST EXPENSE
 
     Interest expense for the first nine months of 1997 amounted to $0.01
million compared to $2.0 million in the same period of 1996. This improvement
results primarily from reduced levels of indebtedness. See "Liquidity and
Capital Resources" below.
 
INCOME TAXES
 
     In the first nine months of 1997, the Company recorded an income tax
benefit of $4.2 million. This amount is comprised of an income tax provision
against pretax income for the nine-month period of $4.5 million and an income
tax benefit of $8.7 million resulting from an adjustment to the deferred tax
asset valuation allowance due to changes in the Company's expectations about the
ultimate realization of its deferred tax assets in years after 1997. The $0.6
million tax benefit recorded in the first nine months of 1996 is comprised of a
provision against pretax income of $2.0 million and a benefit of $2.6 million
resulting from an adjustment to the deferred tax asset account. Excluding the
$8.7 and $2.6 million valuation allowance adjustments referred to above, the
effective tax rate for the nine months ended September 30, 1997 was
approximately 10.8% compared to 9.6% for the nine months ended September 30,
1996. The difference between the statutory federal tax rate of 35 percent and
the effective tax rate is principally due to adjustments to the deferred tax
asset valuation allowance which existed at December 31, 1996 and 1995,
respectively. The Company currently expects improved profitability in 1997
compared to the expectations inherent in the December 31, 1996 deferred tax
asset. The effect of this adjustment reduced the year-to-date 1996 tax provision
by approximately $5.3 million.
 
                                       11
<PAGE>   13
 
OTHER INCOME
 
     Other income in the first nine months of 1997 amounted to $0.7 million
compared to $0.2 million in the same period of 1996. This increase results
primarily from interest income on short-term money market investments.
 
NET INCOME
 
     Net income for the nine months ended September 30, 1997 amounted to $45.6
million, or 19.4% of sales compared to $21.4 million, or 12.0% of sales in the
first nine months of 1996. Both the 1997 and 1996 periods were favorably
impacted by the income tax benefits referred to above.
 
OUTLOOK
 
     On November 11, 1997, one of the Company's competitors announced that it
has signed an agreement to become the principal titanium supplier to Boeing
Commercial Airplane Group. The intent, as reported, is to give Boeing and its
supply community access to titanium mill products at lower prices and shorter
lead times in return for minimum order quantities and long-term pricing.
 
     RMI has historically been a major supplier of aerospace quality titanium to
the Boeing supply community and 1998 orders have already been booked. Boeing
Commercial Aircraft Group is not itself a major direct purchaser of titanium,
acquiring most of its needs through semi-finished or finished parts and
components supplied by a large and diverse group of fabricators and service
centers. RMI had, and continues to have, discussions with Boeing regarding a
potential long-term contract covering the products currently supplied by RMI.
The level of RMI's participation with the Boeing supply community beyond 1998
will depend on a number of factors including the outcome of current discussions
and Boeing's future requirements. While there can be no guarantees as to the
level or duration of its participation, RMI believes that it will continue to be
a significant, albeit reduced, supplier to the Boeing supply community in the
future. In addition to Boeing, RMI is a leading supplier of aerospace quality
titanium to most major domestic and international aerospace manufacturers.
Assuming a continuing robust aerospace market and expected growth in
nonaerospace applications for titanium, RMI believes, but cannot guarantee, that
it will be able to replace the expected but as yet undetermined reduction in
Boeing supply community business.
 
     RMI continues to devote significant resources to develop new markets and
applications for titanium, particularly those in the oil and gas and geothermal
energy production industries. The Company has supplied titanium seamless pipe,
drilling riser systems and stress joints to a number of projects in these
industries. The efforts of the Company's new market development group has
generated in excess of $40 million in income over the past four years. 1997 is
expected to be the best year to date for these efforts. Proving the benefits of
systems made of titanium is an extensive and time-consuming process due the
critical nature of their use in oil and gas projects. However, RMI believes that
the potential is significant. The continued success of these efforts is
dependent on a number of factors including the Company's ability to demonstrate
the advantages of titanium, acceptance of the Company's products by target
industries and the level of oil and gas exploration and production activities.
 
     RMI continues to work closely with several oil companies and engineering
concerns, both domestic and international, to develop other titanium projects or
applications in the oil and gas and geothermal energy production industries. RMI
has entered into several cooperative ventures to encourage and develop titanium
products for use in the oil and gas industry. RMI and one of its alliance
partners, Stolt Comex Seaway, has initiated a joint industry project ("JIP") to
provide definitive data on the design, engineering, manufacture and installation
of titanium riser systems for offshore floating production platforms. This JIP
will provide the participants with a road map for the use of metallic riser
systems utilizing titanium. Due to their interest in these systems a number of
major oil companies are participating in and providing funding for this JIP.
Another of the Company's alliance partners, Energy Ventures, Inc., is working
with RMI on the development of titanium drill pipe for use in horizontal and
extended reach drilling applications.
 
                                       12
<PAGE>   14
 
     RMI's new market efforts are also focusing on the emerging market for
lightweight titanium armor. With reduced force levels worldwide, it has become
increasingly important for the military to improve the transportability of its'
equipment. The use of titanium armor in place of steel is one way to
significantly reduce weight while maintaining good ballistic properties. RMI is
already supplying armor plate, under a long-term contract, for retrofit of armor
components on the Army's M1/A1 Abrams tank. RMI believes that applications such
as this will increase in the future and could represent a significant growth
opportunity for titanium. Realization of this opportunity will depend on a
number of factors including the affordability of titanium for these applications
and future military spending budgets.
 
     The Company's total order backlog as of September 30, 1997 was
approximately $349 million, compared to $328 million at December 31, 1996, an
increase of approximately 6%.
 
     Beginning in the second half of 1995 and continuing through 1996 and the
first three quarters of 1997, the Company has experienced a significant increase
in the volume of incoming orders at increased prices. The Company estimates that
as of September 30, 1997, orders for substantially all of its anticipated 1997
shipments have been booked or shipped at average prices significantly higher
than its 1996 average realized mill product selling price of $11.88 per pound.
The Company's average realized mill product selling price increased to $14.12
per pound in the first nine months of 1997 compared to $11.71 per pound in the
first nine months of 1996. The Company is currently booking orders for titanium
mill products for delivery in 1998 and first half of 1999. Virtually all of the
Company's 1998 anticipated mill product shipments has already been booked, and
is included in the backlog. The increase in demand has been driven primarily by
the recovery in the commercial aerospace market.
 
     Because of competitive factors in the titanium industry and the cyclical
nature of the aerospace industry, including the matters referred to above, there
can be no assurances that prices and demand will remain at current levels or
improve.
 
     The increase in demand for titanium products has put upward pressure on
prices for certain raw materials used by the Company. Prices for the Company's
1997 titanium sponge requirements have been set under long-term supply contracts
and short-term arrangements. Prices for titanium sponge in 1997 have increased
slightly over 1996 levels. The Company is currently finalizing its 1998
arrangements, and no increase in average price is anticipated. Due to increased
demand, prices for titanium scrap, which accounts for approximately 40% of the
Company's raw material requirements, remain somewhat elevated. Increased scrap
generation by fabricators could increase supplies and thereby put downward
pressure on future scrap prices; however, there is no certainty that supplies
will increase or not be offset by other factors. Prices of certain alloying
agents have also increased as a result of increased demand. The Company, and
others, have announced increased prices and surcharges to recover these
increased costs.
 
LIQUIDITY AND CAPITAL RESOURCES
 
     Net cash flows from operating activities totaled $23.7 million in the first
nine months of 1997 compared to $22.3 million used in operations during the
first nine months of 1996. The improvement in net cash flows from operating
activities in the first nine months of 1997, compared to the amount consumed in
the comparable 1996 period is due primarily to significantly improved results of
operations partially offset by increases in working capital. 1996 cash flows
were adversely impacted by significant increases in inventories, accounts
receivable, and the payment of $16.1 million of long term pension liabilities.
Working capital amounted to $175.1 million at September 30, 1997, compared to
$132.1 million at December 31, 1996. The increase in working capital results
primarily from increases in cash, inventory and accounts receivable partially
offset by an increase in accounts payable and other current liabilities. The
Company's working capital ratio was 5.6 to 1 at September 30, 1997.
 
     During the first nine months of 1997, the Company's cash flow requirements
for capital expenditures were funded by cash provided from operating activities.
In the first six months of 1996, the Company's cash flow requirements for
capital expenditures and working capital needs were funded through borrowings
under the existing credit facilities, and proceeds from the Common Stock
Offering referred to below.
 
                                       13
<PAGE>   15
 
     On May 7, 1996, the Company completed a public offering of 4,600,000 shares
of common stock at a price of $18.50 per share (the "Common Stock Offering").
Net proceeds to RMI after deducting underwriting fees and expenses amounted to
$80.3 million. The new proceeds were used to repay all outstanding indebtedness
(amounting to $65.5 million) under the then existing bank credit facilities, and
to contribute $10.2 million to certain of the company's defined benefit pension
plans. The balance was used for general corporate purposes.
 
     On July 3, 1997, the Company acquired 90% of the common stock of Galt
Alloys, Inc., a manufacturer of ferrotitanium and a producer and worldwide
distributor of specialty alloys to ferrous and nonferrous customers. In
connection with this transaction, Galt is undertaking a major expansion program
estimated to cost approximately $20 million, designed to enable Galt to better
serve the titanium industry and its customers. The expansion will include a new
scrap preparation facility, and plasma consolidation furnace, and a plasma
hearth furnace. RMI's investment in Galt amounts to an initial cash investment
of $3 million and an agreement to invest an additional $17 million over the
period required to complete the expansion referred to above which is expected to
be approximately 18-24 months. Additionally, to meet increased demand for its
products, in October 1997 Galt undertook an expansion of its ferro alloy
operations. Cost of the expansion is estimated to be approximately $1.5 million
which is expected to be funded from operating cash flow.
 
     The Company anticipates that it will be able to fund its 1997 working
capital requirements and its capital expenditures primarily from funds generated
by operations. The Company's long-term liquidity requirements, including capital
expenditures, are expected to be financed by a combination of internally
generated funds, borrowings and other sources of external financing if needed.
 
INCOME TAX CONSIDERATIONS
 
     SECTION 382 LIMITATION. At December 31, 1996, the Company had net operating
loss carryforwards of approximately $95 million available to reduce federal
taxable income through 2010. If an "ownership change" were to occur, the
utilization of net operating loss carryforwards would be subject to an annual
limitation. Generally, an ownership change occurs with respect to a corporation
if shareholders who own, directly or indirectly, 5% or more of the capital stock
of the corporation increase their aggregate percentage ownership of such stock
by more than 50 percentage points over the lowest percentage of such stock owned
by such shareholders at any time during a prescribed testing period. Management
does not believe that the sale of shares of Common Stock resulted in an
ownership change. An ownership change could result from equity transactions such
as exercises of stock options, purchases or sales of Common Stock by certain
stockholders, including USX, and other issuances of Common Stock by the Company.
If the annual limitation were to apply, the amount of the limitation would
generally equal the product of (i) the fair market value of the Company's equity
immediately prior to the ownership change, with certain adjustments, including a
possible adjustment to exclude certain capital contributions made in the two
years preceding the date of the ownership change, and (ii) a long-term tax
exempt bond rate of return published monthly by the Internal Revenue Service.
Should the annual limitation apply, the Company believes that it would not
materially affect the potential use of the net operating loss carryforwards to
reduce any future income tax liabilities over time; however, it is possible that
the Company's results in a particular year could exceed the annual limitation,
in which case such excess would not be reduced by the net operating loss
carryforward and the Company's tax liability would be correspondingly higher.
 
     SFAS NO. 109. EFFECTS. SFAS 109 requires a valuation allowance when it is
more likely than not that some portion or all of the deferred tax assets will
not be realized. It further states that forming a conclusion that a valuation
allowance is not needed is difficult when there is negative evidence such as
cumulative losses in recent years. The ultimate realization of all or part of
the Company's deferred income tax assets depends on the Company's ability to
generate sufficient taxable income in the future.
 
     When preparing future periods' interim and annual financial statements, the
Company will periodically evaluate its strategic and business plans, in light of
evolving business conditions, and the valuation allowance will be adjusted for
future income expectations resulting from that process, to the extent different
from those inherent in the current valuation allowance. In making an assessment
of realizability at September 30, 1997,
 
                                       14
<PAGE>   16
 
the Company considered a number of factors including the improved profitability
in 1997 as a result of increased sales, product pricing and gross margins, when
compared to expectations inherent in the December 31, 1996 valuation allowance.
Accordingly, the valuation allowance was adjusted for the difference between
such revised future income expectations and those inherent in the valuation
allowance at December 31, 1996. Additionally, the valuation allowance was
adjusted by $8.7 million at September 30, 1997 because of improving expectations
regarding income in years after 1997 which were not inherent in the valuation
allowance at December 31, 1996. The effect of these adjustments resulted in a
tax benefit of $4.2 million for the nine months ended September 30, 1997.
 
     The application of SFAS No. 109 valuation allowance determination process
could result in recognition of income tax provisions or benefits in a single
interim or annual period due to changes in income expectations over a horizon
that may span several years. Such tax provision or benefit effect could be
material in the context of the specific interim or annual reporting period in
which changes in judgement about more extended future periods are reported. This
effect is a consequence of the application of the SFAS No. 109 valuation
allowance determination process, which is a balance sheet oriented model and
which does not have periodic matching of pretax income or loss and the related
tax effects as an objective.
 
     The Section 382 limitation described above could, if applicable, adversely
impact the income tax provision or benefit in a particular year as a result of
the application of the SFAS No. 109 valuation allowance determination process;
however, it is not expected to have an adverse impact over time.
 
     If the Company's principal markets continue at their improved levels,
additional tax benefits may be reported in future periods, as the valuation
allowance is further reduced. Alternatively, to the extent that the Company's
future profit expectations remain static or are diminished, tax provisions which
more closely approximate the federal statutory tax rate, may be charged against
pretax income. The Company's effective income tax rate will likely increase in
1998 from expected 1997 levels of approximately 10% as available net operating
loss carryforwards are adjusted. It is not possible to accurately predict the
1998 tax rate because of uncertainty surrounding remaining net operating loss
utilization and future levels of profitability. However, as an example, if 1997
profit levels are repeated in 1998, the effective tax rate would be
approximately 20-25%.
 
ENVIRONMENTAL MATTERS
 
     The Company is subject to environmental laws and regulations as well as
various health and safety laws and regulations that are subject to frequent
modifications and revisions. While the costs of compliance for these matters
have not had a material adverse impact on RMI in the past, it is impossible to
predict accurately the ultimate effect these changing laws and regulations may
have on the Company in the future.
 
     At September 30, 1997, the amount accrued for future environmentrelated
costs was $2.6 million. Based on available information, RMI believes its share
of potential environmental-related costs, before expected contributions from
third parties, is in a range from $3.9 million to $6.5 million, in the
aggregate. The amount accrued is net of expected contributions from third
parties (which does not include any amounts from insurers) of approximately $2.1
million, which the Company believes are probable. The Company has received
contributions from such third parties for a number of years as partial
reimbursement for costs incurred by the Company. As these proceedings continue
toward final resolution, amounts in excess of those already provided may be
necessary to discharge the Company from its obligations for these projects.
 
     The ultimate resolution of these environmental matters could individually,
or in the aggregate, be material to the consolidated financial statements.
However, management believes that the Company will remain a viable and
competitive enterprise even though it is possible that these matters could be
resolved unfavorably.
 
CAPITAL EXPENDITURES
 
     Gross capital expenditures the first nine months of 1997 and 1996 amounted
to $4.4 and $2.4 million, respectively. The Company has budgeted capital
spending of approximately $16.0 million in 1997. A similar amount is expected in
1998. RMI anticipates that current capital spending plans can be funded using
cash
 
                                       15
<PAGE>   17
 
provided from internally generated sources supplemented, if required, with
borrowings under the existing credit facility.
 
NEW ACCOUNTING STANDARDS
 
     In February 1997, the Financial Accounting Standards Board (FASB) issued
Statement of Financial Accounting Standards (SFAS) No. 128, "Earnings per
Share." SFAS No. 128 establishes new standards for computing and presenting
earnings per share. The Company is required to adopt the provisions of SFAS No.
128 for its consolidated financial statements beginning with the year ending
December 31, 1997. Upon adoption, the standard also requires the restatement of
all prior period earnings per share information presented.
 
     In June 1997, the FASB issued SFAS No. 130, "Reporting Comprehensive
Income," and SFAS No. 131, "Disclosures about Segments of an Enterprise and
Related Information." SFAS No. 130 establishes standards for reporting and
display of comprehensive income and its components. The Company is required to
adopt the provisions of SFAS No. 130 beginning with its consolidated financial
statements for the three months ending March 31, 1998. SFAS No. 131 requires
certain disclosures about segment information in interim and annual financial
statements and related information about products and services, geographic areas
and major customers. The Company must adopt the provisions of SFAS No. 131 for
its consolidated financial statements for the year ending December 31, 1998.
 
     The results of adopting SFAS No. 128 are not expected to be significant.
 
YEAR 2000 COMPLIANCE
 
     The Company has and will continue to make certain investments in its
application software to ensure the Company is Year 2000 compliant. In addition,
the Company is monitoring the compliance efforts of entities with which it
interacts. While it is not possible, at present, to accurately estimate the
incremental cost of this effort, the Company does not anticipate it will have a
material impact on the long-term results of operations, liquidity or
consolidated financial position of the Company. The discussion of the Company's
efforts and management's expectations relating to the effect of Year 2000
compliance on operating results are forward-looking statements. Actual results
could be materially different because RMI's ability to achieve Year 2000
compliance and the level of incremental costs associated therewith could be
adversely impacted by, among other things, the availability and cost of
programming and testing resources, vendors' ability to modify proprietary
software and unanticipated problems identified in the ongoing compliance review.
In addition, RMI has limited or no control over the actions of proprietary
software vendors and other entities with which it interacts. Therefore, Year
2000 compliance problems experienced by these entities could adversely affect
the results of the Company.
 
                           PART II--OTHER INFORMATION
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.
 
  (a) Exhibits
 
      2.0 Amended and Restated Reorganization Agreement, incorporated by
          reference to Exhibit 2.1 to the Company's Registration Statement on
          Form S-1 No. 33-30667 Amendment No. 1.
 
      3.1 Articles of Incorporation of the Company, as amended June 9, 1997,
          incorporated by reference to Exhibit 10.1 to the Company's Current
          Report on Form 8-K dated June 10, 1997.
 
      3.2 Amended Code of Regulations of the Company, incorporated by reference
          to Exhibit 3.2 to the Company's Annual Report on Form 10-K for the
          year ended December 31, 1993.
 
      4.0 Credit Agreement dated as of April 15, 1996 by and among RMI Titanium
          Company, an Ohio Corporation, and PNC Bank, National Association, as
          agent for the Banks, incorporated by reference to Exhibit 4.1 to the
          Company's Registration Statement on Form S-3 No. 333-01553 Amendment
          No. 2.
 
                                       16
<PAGE>   18
 
      4.1 Rights Agreement (including a Certificate of Adoption of Amendment to
          Amended Articles of Incorporation as Exhibit A thereto, a Form of
          Right Certificate as Exhibit B thereto and a Summary of Rights to
          Purchase Preferred Stock as Exhibit C thereto), incorporated by
          reference to Exhibit 10.1 to the Company's Current Report on Form 8-K
          dated June 10, 1997.
 
      27 Financial Data Schedule
 
  (b) None.
 
                                       17
<PAGE>   19
 
                                   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.
 
                                                   RMI TITANIUM COMPANY
 
                                          --------------------------------------
                                                       (Registrant)
 
Date: November 14, 1997
                                          By:       /s/ T. G. RUPERT
 
                                            ------------------------------------
                                                        T. G. Rupert
                                             Executive Vice President & Chief
                                                    Financial Officer
 
                                       18