<PAGE>

                      SERIES B PREFERRED STOCK AND WARRANT
                               PURCHASE AGREEMENT


          This SERIES B PREFERRED STOCK AND WARRANT PURCHASE AGREEMENT (the
"Agreement") dated September 11, 1998 is entered into by and between Conductus,
Inc., a Delaware corporation (together with its successors, the "Company"), and
the investor set forth on the signature page attached hereto ("Investor").

          Unless otherwise defined herein, capitalized terms used herein and not
defined herein shall have the meanings given to them under the Securities Act of
1933, as amended (the "Securities Act").

          The parties hereto agree as follows:

          1.   PURCHASE AND SALE.  In consideration of and upon the basis of the
representations, warranties and agreements and subject to the terms and
conditions set forth in this Agreement:

               a.   Investor agrees to purchase from the Company, and the
Company agrees to sell to Investor, on the Closing Date specified in Section 2
hereof, the number of shares of the Company's Series B Preferred Stock (the
"Preferred Shares") set forth on the signature page attached hereto for a price
per share equal to $2.70 (the "Purchase Price") and a warrant, in the form
attached hereto as EXHIBIT A, to purchase that number of shares of Common Stock
of the Company equal to 20% of the Preferred Shares purchased hereunder (rounded
to the nearest whole number) at an exercise price per share equal to the
Purchase Price (the "Warrant"). On or before the Closing Date (as defined
below), the Company will have authorized the sale and issuance to Investor of
the Preferred Shares, having the rights, preferences and priviledges set forth
in the Certificate of Designation attached hereto as EXHIBIT B (the "Certificate
of Designation"). The Company and Investor acknowledges and agrees that the
aggregate value of the Warrants and the portion of the purchase price hereunder
to be allocated to the Warrants shall be a total amount equal to $0.03 per
share.

               b.    The term "Conversion Stock" shall mean any shares of the
Company's common stock, par value $0.0001 per share (the "Common Stock"), issued
or to be issued to Investor upon conversion of the Preferred Shares pursuant to
the terms of this Agreement and the Certificate of Designation or upon the
exercise of the Warrant.

          2.   CLOSING.

               a.    The closing of the sale of the Preferred Shares and the
Warrant (the "Closing") shall take place on September 11, 1998 upon satisfaction
or, if applicable, waiver of the conditions set forth in Sections 6 and 7
hereof, or at such other date and time as the Investor and the Company shall
mutually agree (such date and time and any subsequent closing pursuant to
Section being referred to herein as the "Closing Date").

<PAGE>

               b.   At the Closing, the Company shall deliver to Investor (i) a
certificate representing the Preferred Shares that Investor is purchasing and
(ii) the Warrant, duly registered on the books of the Company in the name of
Investor, against payment by Investor of the Purchase Price by check or wire
transfer of immediately available funds.

               c.    The Company may sell up to the balance of the authorized
number of shares of Series B Preferred Stock not sold at the Closing to such
purchasers as it shall select, such new purchasers to become parties hereto by
executing a signature page hereto.

          3.    REPRESENTATIONS AND WARRANTIES OF THE COMPANY.   Except as set
forth in the Disclosure Letter delivered to Investor by the Company concurrently
with this Agreement, the Company hereby represents and warrants to Investor as
follows:

               a.    The Company is a corporation duly organized, validly
existing and in good standing under the laws of the State of Delaware and has
all requisite corporate power and authority to carry on its business as now
conducted and as proposed to be conducted.  The Company is duly qualified to
transact business and is in good standing in each jurisdiction in which the
failure to so qualify would have a material adverse effect on its business or
properties.

               b.    All corporate action on the part of the Company, its
officers and directors necessary for the authorization, execution and delivery
of this Agreement, the performance of all obligations of the Company hereunder
and thereunder, and the authorization, issuance (or reservation for issuance),
sale and delivery of the Preferred Shares and the Warrant being sold hereunder
and the Conversion Stock has been taken or will be taken prior to the Closing,
and this Agreement constitutes a valid and legally binding obligation of the
Company, enforceable in accordance with their respective terms, except (i) as
limited by applicable bankruptcy, insolvency, reorganization, moratorium, and
other laws of general application affecting enforcement of creditors' rights
generally and (ii) as limited by laws relating to the availability of specific
performance, injunctive relief, or other equitable remedies.

               c.    The Company is not in violation or default of any provision
of its Amended and Restated Certificate of Incorporation or bylaws, or of any
judgment, order, writ, or decree by which it is bound. The Company is not in
violation or default in any material respect of any instrument or contract to
which it is a party or by which it is bound, or, to its knowledge, of any
provision of any federal or state statute, rule or regulation applicable to the
Company, which violation or default would have a material adverse effect on its
business or properties.  The execution, delivery and performance of this
Agreement and the consummation of the transactions contemplated hereby will not
result in any such violation or be in conflict with or constitute, with or
without the passage of time and giving of notice, either a default under any
such provision, instrument, judgment, order, writ, decree or contract or an
event that results in the creation of any lien, charge or encumbrance upon any
assets of the Company or the suspension, revocation, impairment, forfeiture, or
nonrenewal of any material permit, license, authorization, or approval
applicable to the Company, its business or operations or any of its assets or
properties.

               d.     No consent, approval, order or authorization of, or
registration, qualification, designation, declaration or filing with, any
federal, state or local governmental 

                                       2

<PAGE>

authority on the part of the Company is required in connection with the 
consummation of the transactions contemplated by this Agreement, except (i) 
the filing of the Certificate of Designation with the Secretary of State of 
Delaware; and (ii) the filing pursuant to Regulation D promulgated by the 
Securities and Exchange Commission under the Securities Act, which filing 
will be effected within 15 days of the sale of the Preferred Shares 
hereunder, or such other post-closing filings as may be required.

               e.    Except as disclosed in the SEC Filings (as defined below)
(i) there is no action, suit, proceeding or investigation pending or, to the
Company's knowledge, currently threatened against the Company that questions the
validity of this Agreement or the right of the Company to enter into such
agreements, or to consummate the transactions contemplated hereby, and (ii)
there is no action, suit, proceeding or investigation pending or, to the
knowledge of the Company, currently threatened in writing against the Company,
or against any executive officer or director of the Company which might result,
either individually or in the aggregate, in any material adverse change in the
business, properties, financial condition or operating results of the Company,
as such business is presently conducted.

               f.    The Company has filed all filings with the United States
Securities and Exchange Commission (the "SEC") under the Securities Act or under
Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended (the
"Exchange Act") or under the rules and regulations promulgated by the SEC (any
such filing, an "SEC Filing") required to be filed by the Company pursuant to
such acts and no SEC Filing contained, on the date on which such document was
filed with the SEC, any untrue statement of a material fact or omitted to state
any material fact required to be stated therein or necessary in order to make
the statements, in the light of the circumstances under which they were made,
not misleading. The financial statements of the Company included in SEC Filings
(including any similar documents filed after the date of this Agreement) comply
as to form in all material respects with applicable accounting requirements and
the published rules and regulations of the SEC with respect thereto, have been
prepared in accordance with generally accepted accounting principles (except, in
the case of unaudited statements, as permitted by Form 10-Q of the SEC) applied
on a consistent basis during the periods involved (except as may be indicated in
the notes thereto), and fairly present the consolidated financial position of
Company and its consolidated subsidiaries as of the dates thereof and the
consolidated results of their operations and cash flows for the periods then
ended (subject, in the case of unaudited statements, to normal year-end audit
adjustments).

               g.   Since the date of the Company's most recent quarterly report
on Form 10-Q or most recent periodic report on Form 8-K filed with the SEC,
there has not been any development that has not otherwise been publicly
disclosed that is reasonably likely to result in any material adverse change in
the financial condition or results of operations of the Company.

               h.    Except as disclosed in the SEC Filings and as contemplated
hereby, the Company has not granted or agreed to grant any registration rights,
including piggy-back rights, to any person or entity.

                                       3

<PAGE>

               i.    As of August 10, 1998, the authorized capital stock of the
Company consisted of 5,000,000 shares of Preferred Stock, none of which were
issued and outstanding, and 20,000,000 shares of Common Stock, 7,116,410 shares
of which were issued and outstanding (the "Preferred Stock" and the "Common
Stock" are collectively referred to herein as the "Capital Stock").  All of the
issued and outstanding shares of Capital Stock have been duly authorized,
validly issued and are fully paid and nonassessable.  There has been no material
change in the capitalization of the Company from August 10, 1998 to the date of
this Agreement.

               j.    The Preferred Shares and the Warrant that are being
purchased by the Investor hereunder, when issued, sold or delivered in
accordance with the terms hereof, for the consideration expressed herein, and
the Conversion Stock, upon issuance in accordance with the terms of the
Certificate of Designation, will be duly and validly issued, fully paid and
nonassessable and will be free of any liens and encumbrances created by the
Company and, subject to the accuracy of the representations of the Investor in
this Agreement, will be issued in compliance with all applicable federal and
state securities laws.

          4.    REPRESENTATIONS  AND WARRANTIES OF INVESTOR.   Investor hereby
represents and warrants to the Company on the date hereof, and agrees with the
Company (unless otherwise specified as provided in the paragraphs below), as
follows:

               a.    Investor understands that no United States federal or state
agency has passed on, reviewed or made any recommendation or endorsement of the
Preferred Shares, the Warrant or the Conversion Stock.

               b.    Investor has full power and authority to enter into this
Agreement and such Agreement constitutes its valid and legally  binding
obligation, enforceable in accordance with its terms, except (i) as limited by
applicable bankruptcy, insolvency, reorganization, moratorium, and other laws of
general application affecting enforcement of creditors' rights generally and
(ii) as limited by laws relating to the availability of specific performance,
injunctive relief, or other equitable remedies.

               c.    This Agreement is made with Investor in reliance upon
Investor's representation to the Company, which by Investor's execution of this
Agreement Investor hereby confirms, that the Preferred Shares to be received by
Investor, the Warrant and the Conversion Stock (collectively, the "Securities")
will be acquired for investment for Investor's own account, not as a nominee or
agent, and not with a present view to the resale or distribution of any part
thereof, and that Investor has no present intention of selling, granting any
participation in, or otherwise distributing the same.  By executing this
Agreement, Investor further represents that Investor does not have any contract,
undertaking, agreement or arrangement with any person to sell, transfer or grant
participations to such person or to any third person, with respect to any of the
Securities.

               d.    Investor is an investor in securities of companies in the
development stage and acknowledges that it can bear the economic risk of its
investment, and has such knowledge and experience in financial or business
matters that it is capable of evaluating 

                                       4

<PAGE>

the merits and risks of the investment in the Securities.  Investor also 
represents it has not been organized for the purpose of acquiring the 
Securities.

               e.    Investor is an "accredited investor" within the meaning of
SEC Rule 501(a) of Regulation D, as presently in effect and all representations
made by Investor in that certain Investor Questionnaire completed by Investor
and delivered to the Company are true and correct in all respects as if made on
the date hereof.

               f.    Investor understands that the Securities are being offered
and sold in reliance on a transactional exemption from the registration
requirements of Federal and state securities laws and that the Company is
relying upon the truth and accuracy of the representations, warranties,
agreements, acknowledgments and understandings of the Investor set forth herein
in order to determine the applicability of such exemptions and the suitability
of the Investor to acquire the Securities.

               g.    Investor understands that the Securities it is purchasing
are characterized as "restricted securities" under the federal securities laws
inasmuch as they are being acquired from the Company in a transaction not
involving a public offering and that under such laws and applicable regulations
such securities may be resold without registration under the Securities Act,
only in certain limited circumstances. In this connection, Investor represents
that it is familiar with SEC Rule 144, as presently in effect, and understands
the resale limitations imposed thereby and by the Securities Act.

               h.    Without in any way limiting the representations set forth
above, Investor further agrees not to make any disposition of all or any portion
of the Securities unless and until the transferee has agreed in writing for the
benefit of the Company to be bound by the terms of this Agreement provided and
to the extent such terms are then applicable, and:

                    (1)   There is then in effect a Registration Statement under
the Securities Act covering such proposed disposition and such disposition is
made in accordance with such Registration Statement; or

                    (2)   (i)  Investor shall have notified the Company of the
proposed disposition and shall have furnished the Company with a detailed
statement of the circumstances surrounding the proposed disposition, and (ii) if
reasonably requested by the Company, Investor shall have furnished the Company
with an opinion of counsel, reasonably satisfactory to the Company that such
disposition will not require registration of such shares under the Securities
Act.  It is agreed that the Company will not require opinions of counsel for
transactions made pursuant to Rule 144 except in circumstances that require a
designation of an entity's status as an "affiliate".

               i.    It is understood that the certificates evidencing the
Securities will bear the following legends:

          "THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
1933, AS AMENDED.  THEY MAY NOT BE SOLD, OFFERED FOR 

                                       5

<PAGE>

SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF A REGISTRATION STATEMENT IN 
EFFECT WITH RESPECT TO THE SECURITIES UNDER SUCH ACT OR AN OPINION OF COUNSEL 
SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED OR UNLESS 
SOLD PURSUANT TO RULE 144 OF SUCH ACT."

               j.    The execution, delivery and performance of this Agreement
and the consummation by Investor of the transactions contemplated hereby do not
and will not (i) result in a violation of Investor's charter documents or bylaws
or (ii) conflict with any material agreement, indenture or instrument to which
Investor is a party, or (iii) result in a violation of any order, judgment or
decree of any court or governmental agency applicable to Investor or, to the
Investor's knowledge, of any law, rule, or regulation. Investor is not required
to obtain any consent or authorization of any governmental agency in order for
it to perform its obligations under this Agreement.

          5.   COVENANTS.

               a.   The Company covenants and agrees with Investor as follows:

                    (1)   For so long as any of the Preferred Shares are
outstanding, and in any case for a period of 40 calendar days thereafter, the
Company will cause its Common Stock to continue to be registered under Sections
12(b) or 12(g) of the Exchange Act, will comply in all respects with its
reporting and filing obligations under said act, and will not take any action or
file any document (whether or not permitted by the Securities Act or the
Exchange Act or the rules thereunder) to terminate or suspend its reporting and
filing obligations under said acts, except as permitted herein. For so long as
any of the Preferred Shares are outstanding, and in any case for a period of 40
calendar days thereafter, the Company will use commercially reasonable efforts
to continue the listing or trading of its Common Stock on the Nasdaq Stock
Market ("Nasdaq") or on a national securities exchange (as defined in the
Exchange Act) and will comply in all respects with the Company's reporting,
filing and other obligations under the bylaws or rules of the National
Association of Securities Dealers and Nasdaq. Notwithstanding the foregoing,
the provisions of this subsection shall not in any way restrict the Company's
ability to negotiate and consummate the consolidation, reorganization or merger
of the Company with or into any other corporation or corporations or a sale,
conveyance, or other disposition of all or substantially all of the Company's
property or business.

                    (2)   The Company will (i) comply with the terms and
conditions of the Preferred Shares as set forth in the Certificate of
Designation and (ii) not amend the Certificate of Designation without the
express written consent of holders of 66 2/3% of the then outstanding Series B
Preferred Stock.

                    (3)   For so long as any of the Preferred Shares and the
Warrant are outstanding, the Company shall at all times reserve and keep
available, free from preemptive rights, out of its authorized but unissued
Common Stock, for issuance upon conversion of such Preferred Shares or upon
exercise of such Warrant, not less than the maximum number of shares of
Conversion Stock then so issuable.

                                       6

<PAGE>

               b.    The Investor covenants and agrees with the Company that (i)
neither Investor nor any of Investor's affiliates nor any person acting on its
or their behalf will at any time offer or sell any Preferred Shares, the Warrant
or any Conversion Stock other than pursuant to registration under the Securities
Act or pursuant to an available exemption therefrom, and (ii) that such Investor
shall report to the Company Sales made pursuant to a registration statement
under Section 6 below.

               c.    The covenants contained in this Section 5 shall terminate
upon the consummation of any consolidation, reorganization or merger of the
Company with or into any other corporation or corporations or a sale,
conveyance, or other disposition of all or substantially all of the Company's
property or business.

               d.    With a view to making available the benefits of certain
rules and regulations of the SEC that may at any time permit the sale of the
restricted securities to the public without registration, the Company agrees to:

                    (1)   Make and keep public information available, as those
terms are understood and defined in Rule 144 under the Securities Act, at all
times after the effective date of the first registration under the Securities
Act filed by the Company for an offering of its securities to the general
public;

                    (2)   Use its best efforts to then file with the SEC in a
timely manner all reports and other documents required of the Company under the
Securities Act and the Exchange Act; and

                    (3)   So long as Investor owns any Preferred Shares, to
furnish to the Investor upon request, a written statement by the Company as to
its compliance with the reporting requirements of said Rule 144 and of the
Securities Act and of the Exchange Act, a copy of the most recent annual or
quarterly report of the Company, and such other reports and documents of the
Company as the Investor may reasonably request in availing itself of any rule or
regulation of the SEC allowing the Investor to sell any such securities without
registration.

          6.   REGISTRATION RIGHTS.

               a.    REGISTRATION OF SHARES.  The Company shall file with the
SEC, as promptly as practicable following the Closing and in any event within
120 days after the Closing, a registration statement under the Securities Act
covering the resale to the public by the Investor of the Conversion Stock (the
"Registration Statement"). The Company shall use its best efforts to cause the
Registration Statement to be declared effective by the SEC as soon as
practicable and in any event within 180 days after the Closing.  The Company
shall cause the Registration Statement to remain effective until the later of 2
years from the Closing Date or such time as all Conversion Stock may be sold
under Rule 144 within a ninety (90) day period (assuming exercise of all
Warrants and conversion of all Preferred Shares) or such earlier time as all of
the Conversion Stock covered by the Registration Statement have been sold
pursuant thereto.

                                       7

<PAGE>

               b.   LIMITATIONS ON REGISTRATION RIGHTS.

                    (1)  The Company may, by written notice to the Investor, (x)
delay the filing or effectiveness of the Registration Statement (for up to a
total of sixty (60) days) or (y) suspend (for up to a total of seventy-five (75)
days  within  any twelve-month period) the Registration Statement  after
effectiveness and require that the Investor immediately cease sales of shares
pursuant to the Registration Statement, in the event and during such period as
the Company determines that the existence of any fact or the happening of any
event (including without limitation pending negotiations relating to, or the
consummation of, a transaction or the occurrence of any other event) would
require additional disclosure of material information by the Company in the
Registration Statement the confidentiality of which the Company has a business
purpose to preserve or which fact or event would render the Company unable to
comply with SEC requirements (in either case, a "Suspension Event").  In the
case of any Suspension Event occurring prior to and delaying the filing of the
Registration Statement, the Company shall file the Registration Statement, the
Company shall be required to keep the Registration Statement effective until the
earlier of (x) such time as all of the shares offered thereby have been disposed
of in accordance with the intended methods of distribution set forth in the
Registration Statement or (y) the period required by Section 6.a above plus an
extended period equal to the number of days during which any such suspension was
in effect.

                    (2)   If the Company delays or suspends the Registration
Statement or requires the Investor to cease sales of shares pursuant to
paragraph (1) above, the Company shall, as promptly as practicable following the
termination of the circumstance which entitled the Company to do so, take such
actions as may be necessary to file or reinstate the effectiveness of the
Registration Statement and/or give written notice to all Investors authorizing
them to resume sales pursuant to the Registration Statement. If as a result
thereof the prospectus included in the Registration Statement has been amended
to comply with the requirements of the Securities Act, the Company shall enclose
such revised prospectus with the notice to Investor given pursuant to this
paragraph 2, and the Investor shall make no offers or sales of shares pursuant
to the Registration Statement other than by means of such revised prospectus.

               c.   REGISTRATION PROCEDURES.

                    (1)   In connection with the filing by the Company of the
Registration Statement, the Company shall furnish to each Investor a copy of the
prospectus, including a preliminary prospectus, in conformity  with  the
requirements of the Securities Act and such additional copies as are reasonably
requested by the Investor.

                    (2)   The Company shall use its best efforts to register or
qualify the Conversion Stock covered by the Registration Statement under the
securities laws of such 

                                       8

<PAGE>

states as the Investor shall reasonably request; PROVIDED, HOWEVER, that the 
Company shall not be required in connection with this paragraph (ii) to 
qualify as a foreign corporation or execute a general consent to service of 
process in any jurisdiction.

                    (3)   If the Company has delivered final prospectuses to the
Investor and after having done so the prospectus is amended to comply with the
requirements of the Securities Act, the Company shall promptly notify the
Investor and, if requested by the Company, the Investor shall immediately cease
making offers or sales of shares under the Registration Statement and return all
prospectuses to the Company. The Company shall promptly provide the Investor
with revised prospectuses and, following receipt of the revised prospectuses,
the Investor shall be free to resume making offers and sales under the
Registration Statement.

                    (4)   The Company shall pay the expenses incurred by it in
complying with its obligations under this Section 6, including all registration
and filing fees, exchange listing fees, fees and expenses of counsel for the
Company, and fees and expenses of accountants for the Company, but excluding (x)
any brokerage fees, selling commissions or underwriting discounts incurred by
the Investor in connection with sales under the Registration Statement and (y)
the fees and expenses of any counsel retained by Investor.

               d.   REQUIREMENTS OF INVESTOR.  The Company shall not be required
to include any Conversion Stock in the Registration Statement unless the
Investor owning such shares furnishes to the Company in writing such information
regarding such Investor and the proposed sale of Conversion Stock by such
Investor as the Company may reasonably request in writing in connection with the
Registration Statement or as shall be required in connection therewith by the
SEC or any state securities law authorities.

               e.    ASSIGNMENT OF RIGHTS.  A Investor may not assign any of its
rights under this Section 6 except in connection with the transfer of some or
all of his or her Preferred Shares or Conversion Stock to a child or spouse, an
affiliated entity, charitable trust or trust for their benefit or to the limited
or general partner of a Investor, PROVIDED each such transferee agrees in a
written instrument delivered to the Company to be bound by the provisions of
this Section 6.

               f.   INDEMNIFICATION.

                    (1)   To the extent permitted by law, the Company shall
indemnify and hold each Investor, the partners or officers, directors and
stockholders of each Investor, legal counsel and accountants for each Investor,
any underwriter (as defined in the Securities Act) for such Investor and each
person, if any, who controls such Investor or 

                                       9

<PAGE>

underwriter within the meaning of the Securities Act or the Exchange Act, 
against any losses, claims, damages or liabilities (joint or several) to 
which they may become subject under the Securities Act, the Exchange Act or 
any state securities laws, insofar as such losses, claims, damages, or 
liabilities (or actions in respect thereof) arise out of or are based upon 
any of the following statements, omissions or violations in connection with 
the Registration Statement (collectively a "Violation"): (i) any untrue 
statement or alleged untrue statement of a material fact contained in such 
registration statement, including any preliminary prospectus  or final 
prospectus contained therein or any amendments  or supplements thereto, (ii) 
the 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 or alleged violation by the Company of the 
Securities Act, the Exchange Act, any state securities laws or any rule or 
regulation promulgated under the Securities Act, the Exchange Act or any 
state securities laws; and the Company will reimburse each such Investor, 
underwriter or controlling person for any legal or other expenses reasonably 
incurred by them in connection with investigating or defending any such loss, 
claim, damage, liability or action; provided, however, that the indemnity 
agreement contained in this subsection 6.f(1) shall not apply to amounts paid 
in settlement of any such loss, claim, damage, liability or action if such 
settlement is effected without the consent of the Company (which consent 
shall not be unreasonably withheld), nor shall the Company be liable in any 
such case for any such loss, claim, damage, liability or action to the extent 
that it arises out of or is based upon a Violation that occurs in reliance 
upon and in conformity with written information furnished expressly for use 
in connection with such registration by any such Investor, underwriter or 
controlling person; provided further, however, that the foregoing indemnity 
agreement with respect to any preliminary prospectus shall not inure to the 
benefit of any Investor or underwriter, or any person controlling such 
Investor or underwriter, from whom the person asserting any such losses, 
claims, damages or liabilities purchased shares in the offering, if the 
Company shall have furnished to the Investor a revised prospectus (by 
amendment or supplement) which cures the defect giving rise to such loss, 
claim, damage or liability and if a copy of such revised prospectus (as then 
amended or supplemented) was not sent or given by or on behalf of such 
Investor or underwriter to such person, if required by law so to have been 
delivered, at or prior to the written confirmation of the sale of the shares 
to such person.

                    (2)   To the extent permitted by law, each selling Investor
shall indemnify and hold harmless the Company, each of its directors, each of
its officers who has signed the registration statement, each person, if any, who
controls the Company within the meaning of the Securities Act, legal counsel and
accountants for the Company, any underwriter, any other Investor selling
securities in such registration statement and any controlling person of any such
underwriter or other Investor, against any losses, claims, damages or 
liabilities (joint or several) to which any of the foregoing persons may 
become subject, under the Securities Act, the Exchange Act or any state 
securities laws, insofar as such losses, claims, damages or liabilities (or 
actions in respect thereto) arise out of or are based upon any Violation, in 
each case to the extent (and only to the extent) that such Violation occurs 
in reliance upon and in conformity with written information furnished by such 
Investor expressly for use in connection with such registration; and each 
such Investor will reimburse any person intended to be indemnified 

                                       10

<PAGE>

pursuant to this subsection 6.f(2), for any legal or other expenses 
reasonably incurred by such person in connection with investigating or 
defending any such loss, claim, damage, liability or action; provided, 
however, that the indemnity agreement contained in this subsection 6.f(2) 
shall not apply to amounts paid in settlement of any such loss, claim, 
damage, liability or action if such settlement is effected without the 
consent of the Investor (which consent shall not be unreasonably withheld), 
provided that in no event shall any indemnity under this subsection 6.f(2) 
exceed the gross proceeds from the offering received by such Investor.

                    (3)   Promptly after receipt by an indemnified party under
this Section 6.f of notice of the commencement of any action (including any
governmental action), such indemnified party will, if a claim in respect thereof
is to be made against any indemnifying party under this Section 6.f, deliver to
the indemnifying party a written notice of the commencement thereof and the
indemnifying party so desires, jointly with any other indemnifying party
similarly noticed, to assume the defense thereof with counsel  mutually
satisfactory to the parties; provided, however, that an indemnified party
(together with all other indemnified parties that may be inappropriate due to
actual or potential differing interests between such indemnified party and any
other party represented by such counsel in such proceeding.  The failure to
deliver written notice to the indemnifying party within a reasonable time of the
commencement of any such action, if prejudicial to its ability to defend such
action, shall relieve such indemnifying party of any liability to  the
indemnified party under this Section 6.f, but the omission so to deliver written
notice to the indemnifying party will not relieve it of any liability that it
may have to any indemnified party otherwise than under this Section 6.f.

                    (4)  If the indemnification provided for in this Section 6.f
is held by a court of competent jurisdiction to be unavailable to an indemnified
party with respect to any loss, liability, claim, damage or expense referred to
herein, then the indemnifying party, in lieu of indemnifying such indemnified
party hereunder, shall contribute to the amount paid or payable by such
indemnified party as a result of such loss, liability, claim, damage or expense
in such proportion as is appropriate to reflect the relative fault of the
indemnifying party on the one hand and of the indemnified party on the other in
connection with the statements or omissions that resulted in such loss,
liability, claim, damage or expense, as well as any other relevant equitable
considerations.  The relative fault of the indemnifying party and of the
indemnified party shall be determined by reference to, among other things,
whether the untrue or alleged untrue statement of a material fact or the
omission to state a material fact relates to information supplied by the
indemnifying party or by the indemnified party and the parties' relevant intent,
knowledge, access to information, and opportunity to correct or prevent such
statement or omission.

                    (5)   Notwithstanding the foregoing, to the extent that the
provisions on indemnification and contribution contained in the underwriting
agreement entered into in connection with the underwritten public offering are
in conflict with the foregoing provisions, the provisions in the underwriting
agreement shall control.

                                       11

<PAGE>

          7.    CONDITIONS PRECEDENT TO INVESTOR'S OBLIGATIONS.  The obligations
of Investor under subsection 1.a of this Agreement are subject to the
fulfillment on or before the Closing of each of the following conditions, unless
expressly waived in writing by the Investor:

               a.    The representations and warranties of the Company contained
in Section 3 shall be true on and as of the Closing with the same effect as
though such representations and warranties had been made on and as of the date
of such Closing, except for representations and warranties made as of a
particular date, which shall be true and correct as of such date.

               b.    The Company shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are
required to be performed or complied with by it on or before the Closing.

               c.    The President of the Company shall deliver to Investor at
the Closing a certificate stating that the conditions specified in Sections 7.a
and 7.b have been fulfilled and stating that there shall have been no material
adverse change in the business, affairs, operations, properties, assets or
financial condition of the Company since the date of this Agreement.

               d.   The Company shall have caused the Certificate of Designation
to be filed with the Secretary of State of the State of Delaware in accordance
with the laws thereof.

               e.    No statute, rule, regulation, executive order, decree,
ruling or injunction shall have been enacted, entered, promulgated or endorsed
by any court or governmental authority of competent jurisdiction which prohibits
the consummation of any of the transactions contemplated by this Agreement.

               f.    The Company shall have delivered to Investor a certificate
representing the Preferred Shares, duly registered on the books of the Company
in the name of the Investor.

               g.   The Company shall have delivered to Investor the Warrant.

               h.    Investor shall have received from Gunderson Dettmer Stough
Villeneuve Franklin & Hachigian, LLP, counsel for the Company, an opinion, dated
as of the Closing Date, in substantially the form attached hereto as EXHIBIT C.

               i.    The Company shall have received aggregate proceeds from the
sale of the Preferred Shares and Warrants in the amount of $4,000,000.

          8.    CONDITIONS PRECEDENT TO THE COMPANY'S OBLIGATIONS.   The 
obligations of the Company to Investor under this Agreement are subject to 
the fulfillment on or before the Closing of each of the following conditions 
by the Investor, unless expressly waived in writing by the Company:

                                       12

<PAGE>

               a.   The representations and warranties of the Investor contained
in Section 4 shall be true on and as of the Closing with the same effect as
though such representations and warranties had been made on and as of the date
of such Closing, except for representations and warranties made as of a
particular date, which shall be true and correct as of such date.

               b.    The Investor shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are
required to be performed or complied with by it on or before the Closing.

               c.    No statute, rule, regulation, executive order, decree,
ruling or injunction shall have been enacted, entered, promulgated or endorsed
by any court or governmental authority of competent jurisdiction which prohibits
the consummation of any of the transactions contemplated by this Agreement.

               d.    The Investor shall have delivered the aggregate Purchase
Price for the Preferred Shares and the Warrant.

               e.   The Company shall have caused the Certificate of Designation
to be filed with the Secretary of State of the State of Delaware in accordance
with the laws thereof.

          9.    FEES AND EXPENSES.  Each of Investor and the Company agrees to
pay its own expenses incident to the performance of its obligations hereunder,
including, but not limited to the fees, expenses and disbursements of such
party's counsel, except as is otherwise expressly provided in this Agreement.

          10.  SURVIVAL OF THE REPRESENTATIONS, WARRANTIES, ETC.  The respective
representations, warranties, and agreements made herein by or on behalf of the
parties hereto shall remain in full force and effect for a period of two years
from the Closing Date, regardless of any investigation made by or on behalf of
the other party to this Agreement or any officer, director or employee of, or
person controlling or under common control with, such party and will survive
delivery of and payment for the Preferred Shares and any Conversion Stock
issuable hereunder.

          11.  TERMINATION.

               a.    This Agreement may be terminated and the transactions
contemplated by this Agreement may be abandoned at any time prior to the Closing
as follows:

                     (i)   by mutual written consent of the Company and the
Investor; or

                     (ii)  by either the Company or the Investor if the Closing
shall not have occurred on or before October 31, 1998 (the "Termination Date");
provided, however, that the right to terminate this Agreement under this
Section 11 shall not be available to any party 

                                       13

<PAGE>

whose failure to fulfill any obligation under this Agreement has been the 
cause of, or resulted in, the failure of the Closing to occur on or before 
the Termination Date.

          b.    In the event of termination of this Agreement by either the
Company or Investor as provided in this Section 11, this Agreement shall
forthwith become void and have no effect, without any liability or obligation on
the part of the Company or Investor, other than the provisions of this
Section 11 and Section 13, and except to the extent that such termination
results from the willful and material breach by a party of any of its
representations, warranties, covenants or agreements set forth  in  this
Agreement.

          12.   NOTICES.   Unless otherwise provided, any notice required or
permitted under this Agreement shall be given in writing and shall be deemed
effectively given upon delivery by confirmed facsimile or reliable international
courier service or upon personal delivery to the party to be notified.

          13.  MISCELLANEOUS.

               a.    This Agreement may be executed in one or more counterparts
and it is not necessary that signatures of all parties appear on the same
counterpart, but such counterparts together shall constitute but one and the
same agreement.

               b.    This Agreement shall inure to the benefit of and be binding
upon the parties hereto, their respective successors and assigns.

               c.    This Agreement shall be governed by, and construed in
accordance with, the internal laws of the State of California without regard to
principles of conflict of laws.

               d.    The provisions of this Agreement are severable, and if any
clause or provision hereof shall be held invalid, illegal or unenforceable in
whole or in part, such invalidity or unenforceability shall not in any manner
affect any other clause or provision of this Agreement.

               e.    The headings of the sections of this document have been
inserted for convenience of reference only and shall not be deemed to be a part
of this Agreement.

               f.    This Agreement (including the terms and conditions of the
Certificate of Designation relating to the Preferred Shares) constitutes the
entire agreement and supersedes all prior agreements and understandings, both
written and oral, between the parties hereto with respect to the subject matter
of this Agreement and is not intended to confer upon any person other than the
parties hereto any rights or remedies hereunder or under the terms of the term
sheets between such parties.

               g.    The term "affiliate" is used herein as defined in Rule
144(a)(1) under the Securities Act.

                                       14

<PAGE>

          IN WITNESS WHEREOF, the parties hereto have duly executed and
delivered this Agreement, all as of the day and year first above written.


                                         CONDUCTUS, INC.



                                         By:
                                            -------------------------------
                                         Name:
                                         Title:


No. of Preferred Shares _____________    INVESTOR



                                         By:
                                            -------------------------------
                                         Name:
                                         Title: