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                                                                    EXHIBIT 10.3
 
                         REGISTRATION RIGHTS AGREEMENT
 
     THIS REGISTRATION RIGHTS AGREEMENT (this "Agreement") is entered into as of
this 21st day of August, 1996, by and between RMI Titanium Company, an Ohio
corporation (the "Company"), and USX Corporation, a Delaware corporation (the
"Shareholder").
 
     WHEREAS, the Company desires to increase the float in the Common Stock, par
value $.01 per share (the "Common Stock"), of the Company;
 
     WHEREAS, to induce the Shareholder to agree to the resale restrictions of
the Shareholder contained in this Agreement, the Company has determined to
provide the registration rights set forth in this Agreement;
 
     NOW, THEREFORE, in consideration of the premises and the mutual covenants
herein contained and other good and valuable consideration, the receipt and
sufficiency of which is hereby acknowledged, the parties hereto hereby agree as
follows:
 
     1. Definitions.  As used herein, the following terms shall have the
following respective meanings:
 
          "Designated Transferee" shall have the meaning set forth in Section 11
     hereof.
 
          "Exchange Act" shall mean the Securities Exchange Act of 1934, as
     amended.
 
          "Holders" shall mean the Shareholder and any Designated Transferees
     who are holders of record of any Registrable Shares, and any combination of
     two or more Holders, and the term "Holder" shall mean any such Person.
 
          "Other Holders" shall mean Persons who subsequent to the date hereof
     acquire more than 5% of the outstanding shares of Common Stock pursuant to
     a transaction with the Company and to whom the Company grants registration
     rights pursuant to a written agreement in connection with such transaction.
 
          "Person" shall mean any individual, corporation, association,
     partnership, group (as defined in Section 13(d)(3) of the Exchange Act),
     joint venture, business trust or unincorporated organization, or a
     governmental agency or authority or political subdivision thereof.
 
          "Registrable Shares" shall mean (i) the 5,483,600 shares of Common
     Stock owned by the Shareholder on the date of this Agreement, and (ii) any
     securities of the Company issued or distributed after the date of this
     Agreement to a Holder in respect of Registrable Shares by way of stock
     dividend or stock split or other distribution, recapitalization or
     reclassification and any securities of the Company acquired by a Holder
     upon exercise or conversion of any such securities. As to any particular
     Registrable Share, such Registrable Share shall cease to be a Registrable
     Share when (w) it shall have been sold, transferred or otherwise disposed
     of or exchanged pursuant to a registration statement under the Securities
     Act, (x) it shall have been distributed to the public pursuant to Rule 144
     (or any successor provision) under the Securities Act, (y) it shall have
     been sold or transferred to a Person other than a Designated Transferee in
     a private transaction effected other than pursuant to a registration
     statement, or (z) it shall have been sold, transferred or otherwise
     disposed of in violation of this Agreement.
 
          "Registration Expenses" shall have the meaning set forth in Section
     7(b) hereof.
 
          "SEC" shall have the meaning set forth in Section 4(c) hereof.
 
          "Securities Act" shall mean the Securities Act of 1933, as amended.
 
     2. Incidental Registrations. (a) Right to Include Registrable Shares.  Each
time the Company shall determine to file a registration statement under the
Securities Act in connection with the proposed offer and sale for cash of shares
of Common Stock either by it or by any holders of shares of Common Stock, the
Company will give prompt written notice of its determination to each Holder and
of such Holder's rights under this Section 2 at least 21 days prior to the
anticipated filing date of such registration statement; provided, however, that
no such notice shall be required if the form of registration statement and the
rules of the SEC would not permit sales of Registrable Shares by the Holders
pursuant to the registration statement. Upon the
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written request of each Holder made at any time not later than 48 hours prior to
the effective date and time of such registration statement (which request shall
specify the number of Registrable Shares intended to be disposed of by such
Holder), the Company will use its reasonable best efforts, as provided in
Section 5 hereof, to effect the registration under the Securities Act of all
Registrable Shares which the Company has been so requested to register by the
Holders thereof; provided, however, that (i) if, at any time after giving
written notice of its intention to register the sale of shares of Common Stock
and prior to the effective date of the registration statement filed in
connection with such registration and relating to a proposed offer and sale of
its Common Stock by the Company, the Company shall determine for any reason not
to proceed with the proposed registration of the Common Stock to be sold by it,
the Company may, at its election, give written notice of such determination to
each Holder of Registrable Shares and thereupon shall be relieved of its
obligation hereunder to register any Registrable Shares in connection with such
registration, and (ii) if such registration involves an underwritten offering
for the registration of the issuance and sale of shares of Common Stock by the
Company, all Holders of Registrable Shares requesting to be included in the
Company's registration must sell their Registrable Shares to the underwriters on
the same terms and conditions as apply to the Company, with such differences,
including any with respect to indemnification and liability insurance, as may be
customary or appropriate in combined primary and secondary offerings. No
registration effected under this Section 2 shall relieve the Company of its
obligations to effect registrations upon request under Section 4 hereof. There
shall be no limit on the number of times that any Holder may participate in
registrations pursuant to this Section 2(a).
 
     (b) Priority in Incidental Registrations.  If a registration pursuant to
this Section 2 involves an underwritten offering and the managing underwriter or
underwriters in good faith advises the Company in writing that, in its opinion,
the number of shares of Common Stock which the Company, the Holders and any
other Persons intend to include in such registration exceeds the largest number
of such shares of Common Stock which can be sold in such offering without having
an adverse effect on such offering (including the price at which such shares of
Common Stock can be sold), then the Company will include in such registration
(i) first, if the registration pursuant to this Section 2 was initiated by any
Person holding shares of Common Stock exercising demand registration rights,
100% of the shares of Common Stock such other Person proposes to sell (except to
the extent the terms of such other Person's registration rights provide
otherwise); (ii) second, 100% of the shares of Common Stock the Company proposes
to sell for its own account; and (iii) third, to the extent that the number of
shares of Common Stock which such other Person exercising demand registration
rights and the Company propose to sell is less than the number of shares of
Common Stock which the Company has been advised can be sold in such offering
without having the adverse effect referred to above, such number of Registrable
Shares which the Holders have requested to be included in such registration and
such number of shares of Common Stock which other Persons have requested to be
included in such registration, in each case pursuant to Section 2(a) hereof or
other piggyback or incidental registration rights and which, in the opinion of
such managing underwriter or underwriters, can be sold without having the
adverse effect referred to above, such number of Registrable Shares and shares
of Common Stock to be included on a pro rata basis among all requesting Holders
and other Persons on the basis of the relative number of shares of Common Stock
beneficially owned (as such term is used in Rule 13d-3 of the Exchange Act) by
such Holders and other Persons.
 
     3. Holdback Agreements.  If the Company shall effect a registration of the
sale of shares of Common Stock by the Company pursuant to an underwritten public
offering, the Holders agree not to effect any sale, transfer or other
disposition (except in connection with such public offering) of shares of Common
Stock, or of any security convertible into or exchangeable or exercisable for
shares of Common Stock (in each case, other than as part of such underwritten
public offering), during the 90-day period (or such lesser period as the
managing underwriter or underwriters may permit) beginning on the effective date
of such registration, if, and to the extent, the managing underwriter or
underwriters of any such offering determines such action is necessary or
desirable to effect such offering and the managing underwriter or underwriters
or the Company gives notice of such determination to the Holders.
 
     4. Registration on Request. (a) Request by Holders.  Upon the written
request of any one or more Holders that the Company effect the registration
under the Securities Act of all or part of such Holders'
 
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Registrable Shares, and specifying the amount (which shall not be less than
1,000,000 Registrable Shares) and the intended method of disposition thereof,
the Company will promptly give notice of such requested registration to all
other Holders of Registrable Shares and, as expeditiously as possible, use its
reasonable best efforts, as provided in Section 5 hereof, to effect the
registration under the Securities Act of the Registrable Shares which the
Company has been so requested to register; provided, however, that the Company
shall not be required to effect more than three registrations pursuant to this
Section 4; provided, further, that the Company shall not be obligated to file a
registration statement relating to a registration request under this Section 4
(i) if the registration request is delivered after delivery of a notice by the
Company of an intended registration of the sale of shares of Common Stock by the
Company and prior to the earlier of 90 days from such notice or the effective
date of the registration statement referred to in such notice, or (ii) within a
period of 180 days after the effective date of any other registration statement
of the Company requested by a Holder pursuant to this Section 4 or pursuant to
which the Holders included Registrable Shares. The Holders initially requesting
a registration pursuant to this Section 4 may, at any time prior to the
effective date of the registration statement relating to such registration,
revoke such request by providing a written notice to the Company revoking such
request; provided, however, that, in the event the Holders shall have made a
written request for a demand registration (i) which is subsequently withdrawn by
the Holders after the Company has filed a registration statement with the SEC in
connection therewith but prior to such demand registration being declared
effective by the SEC or (ii) which is not declared effective solely as a result
of the failure of the Holders to take all actions reasonably required in order
to have the registration and the related registration statement declared
effective by the SEC, then, in any such event, such demand registration shall be
deemed to have been effected for purposes of this Section 4(a).
 
     (b) Registration Statement Form.  If any registration requested pursuant to
this Section 4 which is proposed by the Company to be effected by the filing of
a registration statement Form S-3 (or any successor or similar short-form
registration statement) shall be in connection with an underwritten public
offering, and if the managing underwriter or underwriters shall advise the
Company in writing that, in its opinion, the use of another form of registration
statement or the inclusion in such form of public information concerning the
Company not required by such form is of material importance to the success of
such proposed offering, then such registration shall be effected on such other
form and such other information shall be used or included.
 
     (c) Registration Statement Deemed Effected.  A registration requested
pursuant to this Section 4 will not be deemed to have been effected unless it
has become effective under the Securities Act and has remained effective for 180
days or such shorter period as all the Registrable Shares included in such
registration have actually been sold thereunder. In addition, if within 180 days
after a registration has become effective, the intended method of distribution
of Registrable Shares pursuant to such registration is materially interfered
with by any stop order, injunction or other order or requirement of the
Securities and Exchange Commission (the "SEC") or other governmental agency or
court, or any threat thereof, or by any notice given by the Company pursuant to
Section 5(a)(vi) hereof, such registration will be deemed not to have been
effected for purposes of Section 4(a).
 
     (d) Priority in Requested Registrations.  If a requested registration
pursuant to this Section 4 involves an underwritten offering and the managing
underwriter or underwriters in good faith advises the Holders requesting such
registration and the Company in writing that, in its opinion, the number of
shares of Common Stock requested to be included in such registration (including
shares of Common Stock which are not Registrable Shares) exceeds the largest
number of shares of Common Stock which can be sold in such offering without
having an adverse effect on such offering (including the price at which such
shares of Common Stock can be sold), then the Company will include in such
registration (i) first, 100% of the Registrable Shares requested to be
registered pursuant to Section 4(a) hereof (provided that if the number of
Registrable Shares requested to be registered pursuant to Section 4(a) hereof
exceeds the number which the Holders and the Company have been advised can be
sold in such offering without having the adverse effect referred to above, the
number of such Registrable Shares to be included in such registration by the
Holders shall be allocated pro rata among such Holders on the basis of the
relative number of Registrable Shares each such Holder has requested to be
included in such registration); (ii) second, to the extent that the number of
Registrable Shares requested to be registered pursuant to Section 4(a) hereof is
less than the number of
 
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shares of Common Stock which such Holders and the Company have been advised can
be sold in such offering without having the adverse effect referred to above,
such number of shares of Common Stock the Company requests to be included in
such registration; and (iii) third, to the extent that the number of Registrable
Shares requested to be included in such registration pursuant to Section 4(a)
hereof and the shares of Common Stock which the Company proposes to sell for its
own account are, in the aggregate, less than the number of shares of Common
Stock which such Holders and the Company have been advised can be sold in such
offering without having the adverse effect referred to above, such number of
other shares of Common Stock proposed to be sold by any other Person which, in
the opinion of such managing underwriter or underwriters, can be sold without
having the adverse effect referred to above (provided that if the number of such
shares of Common Stock of such other Persons requested to be registered exceeds
the number which such Holders and the Company have been advised can be sold in
such offering without having the adverse effect referred to above, the number of
such shares of Common Stock to be included in such registration pursuant to this
Section 4(d) shall be allocated pro rata among all such other Persons on the
basis of the relative number of shares of Common Stock each such Person has
requested to be included in such registration).
 
     5. Registration Procedures.  (a) If and whenever the Company is required by
the provisions of Sections 2 or 4 hereof to use its reasonable best efforts to
effect or cause the registration of Registrable Shares, the Company shall as
expeditiously as possible:
 
          (i) prepare and (in the event of a registration requested pursuant to
     Section 4 hereof, as soon as reasonably possible and in any event within 60
     days after the request for registration is given to the Company) file with
     the SEC a registration statement with respect to such Registrable Shares
     and use its reasonable best efforts to cause such registration statement to
     become effective;
 
          (ii) prepare and file with the SEC such amendments and supplements to
     such registration statement and the prospectus used in connection therewith
     as may be necessary to keep such registration statement effective for a
     period not in excess of 180 days and to comply with the provisions of the
     Exchange Act, and the rules and regulations promulgated thereunder, with
     respect to the disposition of all the shares of Common Stock covered by
     such registration statement during such period in accordance with the
     intended methods of disposition by the Holders thereof set forth in such
     registration statement; provided, that (A) before filing a registration
     statement (including an initial filing) or prospectus, or any amendments or
     supplements thereto, the Company will furnish to one counsel selected by
     the Holders of a majority of the Registrable Shares covered by such
     registration statement copies of all documents proposed to be filed, which
     documents will be subject to the review and comment of such counsel, and
     (B) the Company will notify each Holder of Registrable Shares covered by
     such registration statement of any stop order issued or threatened by the
     SEC, any other order suspending the use of any preliminary prospectus or of
     the suspension of the qualification of the registration statement for
     offering or sale in any jurisdiction, and take all reasonable actions
     required to prevent the entry of such stop order, other order or suspension
     or to remove it if entered;
 
          (iii) furnish to each Holder and each underwriter, if applicable, of
     Registrable Shares covered by such registration statement such number of
     copies of the registration statement and of each amendment and supplement
     thereto (in each case including all exhibits), such number of copies of the
     prospectus included in such registration statement (including each
     preliminary prospectus and summary prospectus) in conformity with the
     requirements of the Securities Act, and such other documents as each Holder
     of Registrable Shares covered by such registration statement may reasonably
     request in order to facilitate the disposition of the Registrable Shares
     owned by such Holder;
 
          (iv) use its reasonable best efforts to register or qualify such
     Registrable Shares covered by such registration statement under the state
     securities or blue sky laws of such jurisdictions as each Holder of
     Registrable Shares covered by such registration statement and, if
     applicable, each underwriter, may reasonably request, and do any and all
     other acts and things which may be reasonably necessary to consummate the
     disposition in such jurisdictions of the Registrable Shares owned by such
     Holder, except that the Company shall not for any purpose be required to
     qualify generally to do business as a foreign
 
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     corporation in any jurisdiction where, but for the requirements of this
     clause (iv), it would not be obligated to be so qualified;
 
          (v) use its reasonable best efforts to cause such Registrable Shares
     covered by such registration statement to be registered with or approved by
     such other governmental agencies or authorities as may be necessary to
     enable the Holders thereof to consummate the disposition of such
     Registrable Shares;
 
          (vi) if at any time when a prospectus relating to the Registrable
     Shares is required to be delivered under the Securities Act any event shall
     have occurred as the result of which any such prospectus as then in effect
     would include an untrue statement of a material fact or omit to state any
     material fact required to be stated therein or necessary to make the
     statements therein not misleading, immediately give written notice thereof
     to each Holder and the managing underwriter or underwriters, if any, of
     such Registrable Shares and prepare and furnish to each such Holder a
     reasonable number of copies of an amended or supplemental prospectus as may
     be necessary so that, as thereafter delivered to the purchasers of such
     Registrable Shares, such prospectus shall not include an untrue statement
     of material fact or omit to state a material fact required to be stated
     therein or necessary to make the statements therein not misleading;
 
          (vii) use its reasonable best efforts to list such Registrable Shares
     on any securities exchange on which similar securities of the Company are
     then listed, and enter into customary agreements including a listing
     application and indemnification agreement in customary form, provided that
     the applicable listing requirements are satisfied, and provide a transfer
     agent and registrar for such Registrable Shares covered by such
     registration statement not later than the effective date of such
     registration statement;
 
          (viii) enter into such customary agreements (including an underwriting
     agreement in customary form) and take such other actions as each Holder of
     Registrable Shares being sold or the underwriter or underwriters, if any,
     reasonably request in order to expedite or facilitate the disposition of
     such Registrable Shares, including customary indemnification and opinions;
 
          (ix) use its reasonable best efforts to obtain all "comfort" letters
     and consents from the Company's independent public accountants and all
     legal opinions and consents from the Company's legal counsel and the
     cooperation of other experts, all in customary form and covering matters of
     the type customarily covered by such letters, opinions and experts as such
     Holders or the underwriters retained by such Holders shall reasonably
     request;
 
          (x) make available for inspection by representatives of any Holder of
     Registrable Shares covered by such registration statement, by any
     underwriter participating in any disposition to be effected pursuant to
     such registration statement and by any attorney, accountant or other agent
     retained by such Holders or any such underwriter, all financial and other
     records, pertinent corporate documents and properties of the Company and
     its subsidiaries, and cause all of the Company's and its subsidiaries'
     officers, directors and employees to supply all information and respond to
     all inquiries reasonably requested by such Holders or any such
     representative, underwriter, attorney, accountant or agent in connection
     with such registration statement and to participate in any reasonable
     marketing "road show" presentations which such Holders or the underwriters
     retained by such Holders may request;
 
          (xi) notify counsel for the Holders of Registrable Shares included in
     such registration statement and the managing underwriter or underwriters,
     if any, immediately, and confirm the notice in writing, (A) when the
     registration statement, or any post-effective amendment to the registration
     statement, shall have become effective, or any supplement to the prospectus
     or any amendment prospectus shall have been filed, (B) of the receipt of
     any comments from the SEC and (C) of any request of the SEC to amend the
     registration statement or amend or supplement the prospectus or for
     additional information; and
 
          (xii) in the case of any underwritten public offering pursuant to a
     registration effected pursuant to Section 4 hereof, agree not to effect any
     sale, transfer or other disposition (except in connection with such public
     offering or an offering on Form S-8) of shares of Common Stock or any
     security convertible into or exchangeable or exercisable for shares of
     Common Stock for a 90-day period (or such lesser period as the managing
     underwriter or underwriters may permit) beginning on the effective date of
     such registration, if,
 
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     and to the extent, the managing underwriter or underwriters of any such
     offering determines such action is necessary or desirable to effect such
     offering and the managing underwriter or underwriters or the Holders give
     notice of such determination to the Company.
 
     (b) Each Holder of Registrable Shares hereby agrees that, upon receipt of
any notice from the Company of the happening of any event of the type described
in Section 5(a)(vi) hereof, such Holder shall forthwith discontinue disposition
of such Registrable Shares covered by such registration statement or related
prospectus until such Holder's receipt of the copies of the supplemental or
amended prospectus contemplated by Section 5(a)(vi) hereof, and, if so directed
by the Company, such Holder will deliver to the Company (at the Company's
expense) all copies, other than permanent file copies then in such Holder's
possession, of the prospectus covering such Registrable Shares at the time of
receipt of such notice. In the event the Company shall give any such notice, the
period mentioned in Section 5(a)(ii) hereof shall be extended by the number of
days during the period from and including the date of the giving of such notice
pursuant to Section 5(a)(vi) hereof and including the date when such Holder
shall have received the copies of the supplemental or amended prospectus
contemplated by Section 5(a)(vi) hereof. If for any other reason the
effectiveness of any registration statement filed pursuant to Section 4 hereof
is suspended or interrupted prior to the expiration of the time period regarding
the maintenance of the effectiveness of such registration statement required by
Section 5(a)(ii) hereof so that Registrable Shares may not be sold pursuant
thereto, the applicable time period shall be extended by the number of days
equal to the number of days during the period beginning with the date of such
suspension or interruption to and ending with the date when the sale of
Registrable Shares pursuant to such registration statement may be recommenced.
 
     (c) Each Holder hereby agrees to provide the Company, upon receipt of its
request, with such information about such Holder to enable the Company to comply
with the requirements of Securities Act and to execute such certificates as the
Company may reasonably request in connection with such information and otherwise
to satisfy any requirements of law.
 
     (d) Notwithstanding anything to the contrary contained in this Agreement,
the Company may delay filing a registration statement, and may withhold efforts
to cause the registration statement to become effective, if the Company
determines in good faith that such registration might (i) materially interfere
with or adversely affect the negotiation or completion of any transaction that
is being contemplated by the Company (whether or not a final decision has been
made to undertake such transaction) or any underwritten public offering of
Common Stock which is the subject of a registration that the Company intends to
effect within 30 days after the right to delay is exercised, or (ii) involve
initial or continuing disclosure obligations that might not be in the best
interest of the Company's stockholders.
 
     6. Underwritten Registrations.  Subject to the provisions of Sections 2, 3
and 4 hereof, any of the Registrable Shares covered by a registration statement
may be sold in an underwritten offering at the discretion of the Holder thereof.
In the case of an underwritten offering pursuant to Section 2 hereof, the
managing underwriter or underwriters that will administer the offering shall be
the managing underwriter or underwriters selected by the Company, if such
managing underwriter or underwriters is reasonably satisfactory to the Holders
of a majority of the Registrable Shares to be registered. In the case of any
underwritten offering pursuant to Section 4 hereof, the managing underwriter or
underwriters that will administer the offering shall be the managing underwriter
or underwriters selected by the Holders of a majority of the Registrable Shares
to be registered, if such managing underwriter or underwriters are reasonably
satisfactory to the Company.
 
     7. Expenses. (a) The Registration Expenses of all registrations effected
pursuant to Section 2 and Section 4 hereof shall be borne by (i) the Holders,
collectively, and (ii) by the Company (if the Company sells any shares of Common
Stock in connection with such registration) and by any other Person selling
shares of Common Stock in such registration, collectively, in proportion to the
number of shares of Common Stock (or if equity securities other than Common
Stock are included in such registration, based upon the relative aggregate
offering price of all securities included in such registration) included in such
registration.
 
     (b) The Registration Expenses shall include, without limitation, all
out-of-pocket expenses incident to the Company's performance of or compliance
with this Agreement, including without limitation all SEC and stock exchange
registration and filing fees and expenses, reasonable fees and expenses of any
"qualified
 
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independent underwriter" and its counsel as may be required by the rules of the
National Association of Securities Dealers, Inc., fees and expenses of
compliance with securities or blue sky laws (including without limitation
reasonable fees and disbursements of counsel for the underwriters, if any, in
connection with blue sky qualifications of the Registrable Shares), rating
agency fees, printing expenses, the fees and expenses incurred in connection
with the listing of the shares of Common Stock to be registered on each
securities exchange or national market system on which shares of Common Stock
issued by the Company are then listed, fees and disbursements of counsel for the
Company and all independent certified public accountants (including the expenses
of any special audit and "cold comfort" letters required by or incident to such
performance and compliance), securities laws liability insurance (if the Company
decides to obtain such insurance and the Holders are named insureds of such
insurance), the fees and disbursements of the underwriters (including, without
limitation, expenses relating to "road shows" and other marketing activities),
and the reasonable fees and expenses of any special experts and other Persons
retained by the Company in connection with such registration; provided, however,
that Registration Expenses shall not include (i) any allocation of the overhead
of the Company, including any allocation of the compensation or benefits of
employees of the Company that assist in a registration, or (ii) any other
expense to the extent it would have been incurred by the Company in the absence
of any sale of shares of Common Stock in connection with such registration
(including the cost of the Company's annual audit and its preparation of
quarterly financial statements), or (iii) if the Company is selling any shares
of Common Stock in connection with such registration, the fees and disbursements
of counsel for the Company and any fees and expenses incurred in connection with
the listing of such shares sold by the Company on any securities exchange or
national market system .
 
     (c) The Holders shall bear the following expenses of all registrations
effected pursuant to Section 2 and Section 4 hereof: (i) any underwriting
discounts or commissions or transfer taxes, if any, attributable to the sale of
Registrable Shares by the Holders, and (ii) the fees of counsel retained in
connection with each such registration by the Holders.
 
     8. Indemnification. (a) Indemnification by the Company.  In the event of
any registration of any shares of Common Stock of the Company under the
Securities Act pursuant to Sections 2 or 4 hereof, the Company will, and it
hereby does, indemnify and hold harmless, to the extent permitted by law, each
of the Holders of any Registrable Shares covered by such registration statement,
each affiliate of such Holder and their respective directors and officers or
general and limited partners (and the directors, officers, general and limited
partners, affiliates and controlling Persons thereof), each other Person who
participates as an underwriter in the offering or sale of such shares of Common
Stock and each other Person, if any, who controls such Holder or any such
underwriter within the meaning of the Securities Act (collectively, the
"Indemnified Parties"), against any and all losses, claims, damages or
liabilities, joint or several, and expenses (including any amounts paid in any
settlement effected with the Company's consent, which consent shall not be
unreasonably withheld) to which any Indemnified Party may become subject under
the Securities Act, state securities or blue sky laws, common law or otherwise,
insofar as such losses, claims, damages or liabilities (or actions or
proceedings in respect thereof, whether or not such Indemnified Party is a party
thereto) or expenses arise out of or are based upon (i) any untrue statement or
alleged untrue statement of any material fact contained in any registration
statement under which such shares of Common Stock were registered under the
Securities Act, any preliminary, final or summary prospectus contained therein,
or any amendment or supplement thereto, (ii) any omission or alleged omission to
state therein a material fact required to be stated therein or necessary to make
the statements therein not misleading or (iii) any violation by the Company of
any federal, state or common law rule or regulation applicable to the Company
and relating to action required of or inaction by the Company in connection with
any such registration, and the Company will reimburse such Indemnified Party for
any reasonable legal or any other expenses incurred by it in connection with
investigating or defending any such loss, claim, liability, action or
proceeding; provided, that the Company shall not be liable to any Indemnified
Party in any such case to the extent that any such loss, claim, damage,
liability (or action or proceeding in respect thereof) or expense arises out of
or is based upon any untrue statement or alleged untrue statement or omission or
alleged omission made in such registration statement or amendment or supplement
thereto or in any such preliminary, final or summary prospectus in reliance upon
and in conformity with written information with respect to such Holder furnished
to the Company by such Holder specifically for use in the preparation thereof.
Such indemnity shall remain in full force and effect
 
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<PAGE>   8
 
regardless of any investigation made by or on behalf of such Holder or any
Indemnified Party and shall survive the transfer of such securities by such
Holder.
 
     (b) Indemnification by the Holders and Underwriters.  The Company may
require, as a condition to including any Registrable Shares in any registration
statement filed in accordance with Sections 2 or 4 hereof, that the Company
shall have received an undertaking reasonably satisfactory to it from the
Holders of such Registrable Shares or any underwriter to indemnify and hold
harmless (in the same manner and to the same extent as set forth in Section 8(a)
hereof) the Company with respect to any statement or alleged statement in or
omission or alleged omission from such registration statement, any preliminary,
final or summary prospectus contained therein, or any amendment or supplement,
if such statement or alleged statement or omission or alleged omission was made
in reliance upon and in conformity with written information with respect to the
Holders of the Registrable Shares being registered or such underwriter furnished
to the Company by such Holders or such underwriter specifically for use in the
preparation of such registration statement, preliminary, final or summary
prospectus or amendment or supplement, or a document incorporated by reference
into any of the foregoing. Such indemnity shall remain in full force and effect
regardless of any investigation made by or on behalf of the Company or any of
the Holders, or any of their respective affiliates, directors, officers or
controlling Persons, and shall survive the transfer of such securities by such
Holder.
 
     (c) Notices of Claims, Etc.  Promptly after receipt by an indemnified party
hereunder of written notice of the commencement of any action or proceeding with
respect to which a claim for indemnification may be made pursuant to this
Section 8, such indemnified party will, if a claim in respect thereof is to be
made against an indemnifying party, give written notice to the latter of the
commencement of such action; provided, that the failure of the indemnified party
to give notice as provided herein shall not relieve the indemnifying party of
its obligations under Section 8(a) or (b), except to the extent that the
indemnifying party is actually materially prejudiced by such failure to give
notice. In case any such action is brought against an indemnified party, the
indemnifying party will be entitled to participate in and to assume the defense
thereof, with counsel satisfactory to such indemnified party, and after notice
from the indemnifying party to such indemnified party of its election so to
assume the defense thereof, the indemnifying party will not be liable to such
indemnified party for any legal or other expenses subsequently incurred by the
latter in connection with the defense thereof other than reasonable costs of
investigation; provided, that the indemnified party shall have the right to
employ counsel to represent the indemnified party and its respective controlling
persons, directors, officers, general or limited partners, employees or agents
who may be subject to liability arising out of any claim in respect of which
indemnity may be sought by the indemnified party against such indemnifying party
under this Section 8 if (i) the employment of such counsel shall have been
authorized in writing by such indemnifying party in connection with the defense
of such action, (ii) the indemnifying party shall not have promptly employed
counsel reasonably satisfactory to the indemnified party to assume the defense
of such action or counsel, or (iii) any indemnified party shall have been
advised in writing by outside counsel reasonably satisfactory to the
indemnifying party that there may be defenses available to such indemnified
party or its respective controlling persons, directors, officers, employees or
agents which are in conflict with those available to the indemnifying party, and
in that event the reasonable fees and expenses of one firm of separate counsel
for the indemnified party (in addition to the reasonable fees and expenses of
one party serving as local counsel) shall be paid by the indemnifying party. No
indemnifying party will consent to entry of any judgment or enter into any
settlement which does not include as an unconditional term thereof the giving by
the claimant or plaintiff to such indemnified party of a release from all
liability in respect to such claim or litigation.
 
     (d) Contribution.  If the indemnification provided for in this Section 8
shall for any reason be unavailable to any indemnified party under Section 8(a)
or 8(b) hereof or is insufficient to hold it harmless in respect of any loss,
claim, damage or liability, or any action in respect thereof referred to
therein, then each indemnifying party shall contribute to the amount paid
payable by such indemnified party as a result of such loss, claim, damage or
liability, or action in respect thereof, (i) in such proportion as shall be
appropriate to reflect the relative benefits received by the indemnified party
and indemnifying party, and (ii) if the allocation provided by clause (i) above
is not permitted by applicable law, in such proportion as is appropriate to
reflect not only the relative benefits referred to in clause (i) but also the
relative fault of the indemnified party and indemnifying party with respect to
the statements or omissions which resulted in such loss, claim, damage or
liability, or action in respect thereof, as well as any other relevant equitable
considerations. Notwithstanding
 
                                        8
<PAGE>   9
 
any other provision of this Section 8(d), no Holder of Registrable Shares shall
be required to contribute an amount greater than the dollar amount of the
proceeds received by such Holder with respect to the sale of any such
Registrable Shares. No person guilty of fraudulent misrepresentation (within the
meaning of Section 11(f) of the Securities Act) shall be entitled to
contribution from any person who was not guilty of such fraudulent
misrepresentation.
 
     (e) Other Indemnification.  Indemnification similar to that specified in
the preceding subdivisions of this Section 8 (with appropriate modifications)
shall be given by the Company and each Holder of Registrable Shares with respect
to any required registration or other qualification of securities under any
federal or state law or regulation or governmental authority other than the
Securities Act.
 
     (f) Non-Exclusivity.  The obligations of the parties under this Section 8
shall be in addition to any liability which any party may otherwise have to any
other party.
 
     9. Rule 144.  The Company will file in a timely manner the reports required
to be filed by it under the Securities Act and the Exchange Act and the rules
and regulations promulgated thereunder (or, if the Company is not required to
file such reports, it will, upon the request of any Holder of Registrable
Shares, make publicly available such information), and it will take such further
action as any Holder of Registrable Shares may reasonably request, all to the
extent required from time to time to enable such Holder to sell Registrable
Shares without registration under the Securities Act within the limitation of
the exemptions provided by (a) Rule 144 under the Securities Act, as such Rule
may be amended from time to time, or (b) any similar rule or regulation
hereafter adopted by the SEC. Upon the request of any Holder of Registrable
Shares, the Company will deliver to such Holder a written statement as to
whether it has complied with such requirements.
 
     10. Certain Restrictions on Sales.  Notwithstanding anything contained in
this Agreement to the contrary, neither the Shareholder nor any Designated
Transferee shall sell, transfer or otherwise dispose of any Common Stock
(including the Registrable Shares) after the date hereof and on or prior to July
26, 1997 without the prior written consent of the Company, which consent will
not be withheld if the Company determines, in its reasonable discretion, that
the proposed sale, transfer or other disposition of Registrable Shares would not
be inconsistent with the Company's proposed utilization of its net operating
losses for federal income tax purposes.
 
     11. Assignability.  This Agreement shall be binding upon and shall inure to
the benefit of the parties hereto and their respective successors and permitted
assigns as provided in this Section 11. The Holders may assign their rights
under this Agreement, in whole or in part, only to a Person (a "Designated
Transferee") (a) who (i) is an affiliate of the Shareholder or (ii) is not an
affiliate of the Shareholder but the transfer to whom is consented to in writing
by the Company, (b) who is a transferee of Registrable Shares, and (c) who
agrees to be bound by the terms of this Agreement. Any purported assignment in
violation of the Section shall be void.
 
     12. Notices.  Any and all notices or any other communications shall be
given in writing by either (a) personal delivery to and receipted for by the
addressee or by (b) telecopy or registered certified mail which shall be
addressed, in the case of the Company, to: Timothy G. Rupert, Senior Vice
President and Chief Financial Officer, RMI Titanium Company, 1000 Warren Avenue,
Niles, Ohio 44446; and, in the case of the Holders, to: Dan D. Sandman, General
Counsel and Secretary, USX Corporation, 600 Grant Street, Pittsburgh,
Pennsylvania 15219. All such notices and communications shall be deemed to have
been duly given and effective (i) when delivered by hand, if personally
delivered; (ii) two business days after being deposited in the mail, postage
prepaid, if mailed; and (iii) when receipt is acknowledged, if telecopied.
 
     13. No Inconsistent Agreements.  The Company will not hereafter enter into
any agreement with respect to its Common Stock which is inconsistent with the
rights granted to the Holders in this Agreement.
 
     14. Specific Performance.  The Company acknowledges that the rights granted
to the Holders in this Agreement are of a special, unique and extraordinary
character, and that any breach of this Agreement by the Company could not be
compensated for by damages. Accordingly, if the Company breaches its obligations
under this Agreement, the Holders shall be entitled, in addition to any other
remedies that they may have, to
 
                                        9
<PAGE>   10
 
enforcement of this Agreement by a decree of specific performance requiring the
Company to fulfill its obligations under this Agreement.
 
     15. Severability.  If any provision of this Agreement or any portion
thereof is finally determined to be unlawful or unenforceable, such provision or
portion thereof shall be deemed to be severed from this Agreement. Every other
provision, and any portion of such an invalidated provision that is not
invalidated by such a determination, shall remain in full force and effect.
 
     16. Counterparts.  This Agreement may be executed in or more counterparts,
each of which shall be deemed an original and all of which, together, shall
constitute one and the same instrument.
 
     17. Defaults.  A default by any Holder in such Holder's compliance with any
of the conditions or covenants hereof or performance of any of the obligations
of such Holder hereunder shall not constitute a default by any other Holder.
 
     18. Amendments, Waivers. (a) Generally.  This Agreement may not be amended,
modified or supplemented and no waivers of or consents to departures from the
provisions hereof may be given unless consented to in writing by the Company and
the holders of a majority of the Registrable Shares.
 
     (b) Upon Issuance or Distribution of Other Equity Securities.  If, after
the date of this Agreement, the Company issues or distributes any equity
security other than Common Stock by way of stock dividend or stock split or
other distribution, recapitalization or reclassification, the Company and the
Shareholder shall agree upon appropriate additions to and modifications of this
Agreement to (i) preserve to the Shareholder all of the benefits of this
Agreement and (ii) extend to the Shareholder similar rights with respect to such
other securities as are provided in this Agreement to the Shareholder with
respect to the Common Stock if the Company registers shares of such other
security.
 
     19. Captions.  The captions contained in this Agreement are for reference
purposes only and are not part of this Agreement.
 
     20. Entire Agreement.  This Agreement contains the entire agreement among
the parties hereto with respect to the transactions contemplated herein and the
understandings among the parties relating to the subject matter hereof. Any and
all previous agreements and understandings between or among the parties hereto
regarding the subject matter hereof are, whether written or oral, superseded by
this Agreement.
 
     21. Governing Law.  This Agreement is made pursuant to and shall be
construed in accordance with the laws of the State of Ohio. The parties hereto
submit to the jurisdiction of the courts of the State of Ohio in any action or
proceeding arising out of or relating to this Agreement.
 
     IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
executed by their respective authorized officers as of the date aforesaid.
 
                                          RMI TITANIUM COMPANY
 
                                              
                                          By: /s/ T. G. RUPERT
                                              ---------------------------
                                              Name: T. G. Rupert
                                              Title: Executive Vice President
                                                     and Chief Financial Officer
 
                                          USX CORPORATION
 
                                              
                                          By: /s/ G. R. HAGGERTY
                                              ---------------------------
                                              Name: G. R. Haggerty
                                              Title: Vice President and
                                                     Treasurer
 
                                       10