<PAGE>

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                    FORM 10-Q

(Mark One)

[ X ]      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
           EXCHANGE ACT OF 1934

                  For the quarterly period ended March 31, 1999

                                       OR

[   ]      TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
           EXCHANGE ACT OF 1934

               For the transition period from ________ to ________

                         COMMISSION FILE NUMBER 0-11915

                                 CONDUCTUS, INC.
             (Exact name of registrant as specified in its charter)

               DELAWARE                             77-0162388
      (State or other jurisdiction of             (I.R.S. Employer
     incorporation or organization)              Identification No.)

                                969 W. MAUDE AVE.
                               SUNNYVALE, CA 94086
                    (Address of principal executive offices)

                                 (408) 523-9950
                         (Registrant's telephone number)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Sections 13 or 15(d) of the Securities Exchange Act of 1934
during the preceding 12 months (or for such shorter period that the registrant
was required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days: Yes  X  No
                                       ---     ---

As of April 30, 1999 there were 7,144,251 shares of the Registrants Common stock
outstanding.

<PAGE>

                                CONDUCTUS, INC.

                                   FORM 10-Q

                                 March 31, 1999

                                     INDEX
<TABLE>
<CAPTION>
                                                                                                                Page
                                                                                                                ----
<S>                                                                                                             <C>
PART I.     FINANCIAL INFORMATION

Item 1:     Financial Statements...................................................................................1

            Condensed Balance Sheets at March 31, 1999 and December 31, 1998.......................................1

            Condensed Statements of Operations for the Three Months Ended March 31, 1999 and 1998..................2

            Condensed Statements of Cash Flows for the Three Months Ended March 31, 1999 and 1998..................3

            Notes to Condensed Financial Statements................................................................4

Item 2:     Management's Discussion and Analysis of Financial Condition and Results of Operations..................8

Item 3:     Quantitative and Qualitative Disclosures About Market Risk............................................12

PART II:    OTHER INFORMATION

Item 1:     Legal Proceedings.....................................................................................13

Item 2:     Changes in Securities.................................................................................13

Item 3:     Default upon Senior Securities........................................................................13

Item 4:     Submission of Matters to a vote of Security Holders...................................................13

Item 5:     Other Information.....................................................................................13

Item 6:     Exhibits and Reports on Form 8-K......................................................................14
</TABLE>

<PAGE>

PART I:  FINANCIAL INFORMATION

Item 1:  Financial Statements

                                 CONDUCTUS, INC.
                            CONDENSED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                        MARCH 31,            DECEMBER 31,
                                                                          1999                  1998
                                                                  -------------------    -------------------
                                                                       (Unaudited)
<S>                                                               <C>                    <C>
ASSETS
Current assets:
    Cash and cash equivalents...............................      $       989,625        $     1,547,169
    Short-term investments..................................              557,727              1,341,014
    Accounts receivable ....................................            1,079,625              1,109,794
    Inventories.............................................              706,459                842,384
    Prepaid expenses and other current assets...............              117,161                145,470
                                                                  ------------------     ------------------
      Total current assets..................................            3,450,597              4,985,831
    Property and equipment, net.............................            1,815,877              2,020,324
    Other assets............................................               32,131                 28,800
                                                                  -----------------      ------------------
      Total assets..........................................      $     5,298,605        $     7,034,955
                                                                  ==================     ==================

LIABILITIES
Current liabilities:
    Current portion of long-term debt.......................      $       854,050        $       892,139
    Accounts payable........................................              492,807                658,982
    Other accrued liabilities...............................              860,905                778,758
                                                                  ------------------     ------------------
      Total current liabilities.............................            2,207,762              2,329,879
    Long-term debt, net of current portion..................            1,165,803              1,341,407
                                                                  ------------------     ------------------
      Total liabilities.....................................            3,373,565              3,671,286
                                                                  ------------------     ------------------

STOCKHOLDERS' EQUITY
Preferred stock.............................................            5,736,124              5,683,461
Common stock................................................                  714                    714
Additional paid-in capital..................................           42,278,497             42,278,423
Accumulated deficit.........................................          (46,090,295)           (44,598,929)
                                                                  ------------------     ------------------
      Total stockholders' equity............................            1,925,040              3,363,669
                                                                  ------------------     ------------------
      Total liabilities and stockholders' equity............      $     5,298,605        $     7,034,955
                                                                  ==================     ==================
</TABLE>

   The accompanying notes are an integral part of these financial statements.

<PAGE>

                                 CONDUCTUS, INC.
                       CONDENSED STATEMENTS OF OPERATIONS

                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                             THREE MONTHS ENDED MARCH 31,
                                                                      ------------------------------------------
                                                                             1999                    1998
                                                                      -------------------     ------------------
<S>                                                                   <C>                     <C>
Revenues:
  Contract.....................................................       $      917,607          $      863,614
  Product sales................................................              396,770                 264,078
                                                                      -------------------     ------------------
      Total revenues...........................................            1,314,377               1,127,692
                                                                      -------------------     ------------------
Costs and expenses:
    Cost of product sales......................................              569,667                 338,817
    Research and development...................................            1,121,295               2,298,252
    Selling, general and administrative........................              834,470               1,097,803
                                                                      -------------------     ------------------
      Total costs and expenses.................................            2,525,435               3,734,872
                                                                      -------------------     ------------------
Loss from operations...........................................           (1,211,055)             (2,607,180)
Interest income................................................               25,744                  28,599
Other income (expense).........................................                2,505                      --
Interest expense...............................................              (96,880)                (55,623)
                                                                      -------------------     ------------------
    Net loss...................................................           (1,279,686)             (2,634,204)
Preferred dividend.............................................             (211,680)                     --
                                                                      -------------------     ------------------
Net loss attributable to common shareholders...................       $   (1,491,366)         $   (2,634,204)
                                                                      ===================     ==================
Basic and diluted net loss per share...........................       $        (0.21)         $        (0.38)
                                                                      ===================     ==================
Shares used in per share calculations..........................            7,144,162               7,014,625
                                                                      ===================     ==================
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                     2
<PAGE>

                                 CONDUCTUS, INC.
                       CONDENSED STATEMENTS OF CASH FLOWS

                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                                  THREE MONTHS ENDED
                                                                                       MARCH 31,
                                                                        --------------------------------------
                                                                              1999                  1998
                                                                        ---------------        ---------------
<S>                                                                     <C>                    <C>
Cash flows from operating activities:
   Net loss.......................................................      $   (1,279,686)        $   (2,634,204)
    Adjustments to reconcile net loss to net cash used in
      operating activities:
    Depreciation and amortization.................................             212,783                195,999
    Amortization of discount on long term debt....................              11,349                     --
    Provision for excess and obsolete inventories.................                  --                109,895
(Increase) decrease in:
    Accounts receivable...........................................              30,169                562,986
    Inventories...................................................             135,926               (372,581)
    Prepaid expenses and other current assets.....................              28,309                 24,705
    Other assets..................................................              (3,331)                 5,496
Increase, (decrease) in:
    Accounts payable and other accrued liabilities................            (184,708)               631,544
                                                                        ------------------     -----------------
          Net cash used in operating activities...................          (1,071,886)            (1,476,160)
                                                                        ------------------     -----------------
Cash flows from investing activities:
    Maturities of short-term investments..........................             783,287                556,633
    Purchases of short-term investments...........................                  --                     --
    Acquisition of property and equipment.........................              (8,338)              (181,646)
                                                                        ------------------     -----------------
          Net cash provided by investing activities...............             774,949                374,987
                                                                        ------------------     -----------------
Cash flows from financing activities:
    Net proceeds from issuance of common stock....................                  74                 16,685
    Costs to register preferred stock.............................             (58,337)                    --
    Principal repayments on long-term debt........................            (202,344)              (335,426)
                                                                        ------------------     -----------------
          Net cash used in financing activities...................            (260,607)              (318,741)
                                                                        ------------------     -----------------
    Net decrease in cash and cash equivalents.....................            (557,544)            (1,419,914)
Cash and cash equivalents at beginning of period..................           1,547,169              2,611,560
                                                                        ------------------     -----------------
Cash and cash equivalents at end of period........................      $      989,625         $    1,191,646
                                                                        ==================     =================
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                     3
<PAGE>

                                 CONDUCTUS, INC.
                     NOTES TO CONDENSED FINANCIAL STATEMENTS

                                   (Unaudited)

1.          SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES:

UNAUDITED INTERIM FINANCIAL INFORMATION:

            The accompanying unaudited interim financial statements have been
prepared pursuant to the rules and regulations of the Securities and Exchange
Commission. Certain information and footnote disclosures normally included in
the financial statements prepared in accordance with generally accepted
accounting principles have been condensed or omitted pursuant to such rules and
regulations. The unaudited financial statements as of March 31, 1999 and for the
three months ended March 31, 1999 and 1998 include, in the opinion of
management, all adjustments, consisting of normal recurring adjustments,
necessary to present fairly the financial information set forth herein. The
results of operations for the interim periods are not necessarily indicative of
the results to be expected for an entire year. The December 31, 1998 balance
sheet was derived from audited financial statements, but does not include all
disclosures required by generally accepted accounting principles.

BASIC AND DILUTED LOSS PER SHARE:

            In accordance with the disclosure requirements of Statement of
Financial Accounting Standards No. 128 (SFAS 128) "Earnings Per Share," a
reconciliation of the numerator and denominator of the basic and diluted EPS is
provided as follows:

<TABLE>
<CAPTION>
                                                                                     THREE MONTHS ENDED
                                                                                          MARCH 31,
                                                                         -------------------------------------------
                                                                                1999                   1998
                                                                         --------------------   --------------------
<S>                                                                      <C>                    <C>
Numerator - basic and diluted net loss per share:
      Net loss attributable to common shareholders....................    $     (1,491,366)      $    (2,634,204)
Denominator - basic and diluted net loss per share:
      Weighted average common shares outstanding......................           7,144,162             7,014,625
      Basic and diluted net loss per share............................    $          (0.21)      $         (0.38)
</TABLE>

            In the above computations, common equivalent shares are excluded
from the diluted loss per share as their effect is anti-dilutive. Common
equivalent shares including common stock options, warrants and convertible
preferred stock that could potentially dilute basic earnings per share in the
future and that were not included in the computations of diluted loss per share
because of anti-dilution were approximately 1,822,000 and 126,000 for the three
months ended March 31, 1999 and 1998, respectively.

                                     4
<PAGE>

                                 CONDUCTUS, INC.
               NOTES TO CONDENSED FINANCIAL STATEMENTS (CONTINUED)

                                   (Unaudited)

1.          SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (CONTINUED):

RECENT PRONOUNCEMENTS:

            In March 1998, the American Institute of Certified Public
Accountants issued Statement of Position 98-1, "Accounting for the Costs of
Computer Software Developed or Obtained for Internal Use." This standard
requires companies to capitalize qualifying computer software costs which are
incurred during the application development stage and amortize them over the
software's estimated useful life. Statement of Position 98-1 is effective for
fiscal years beginning after December 15, 1998. The adoption of Statement of
Position 98-1 had no impact on the Company's financial statements.

            In April 1998, the American Institute of Certified Public
Accountants issued Statement of Position 98-5, "Reporting on the Costs of
Start-Up Activities." This standard requires companies to expense the costs of
start-up activities and organization costs as incurred. In general, Statement of
Position 98-5 is effective for fiscal years beginning after December 15, 1998.
The adoption of Statement of Position 98-5 had no impact on the Company's
financial statements.

            In June 1998, the Financial Accounting Standards Board issued
Statement of Financial Accounting Standards No. 133, "Accounting for Derivative
Instruments and Hedging Activities." This statement establishes new standards of
accounting and reporting for derivative instruments and hedging activities. This
statement requires that all derivatives be recognized at fair value in the
statement of financial position, and that the corresponding gains or losses be
reported either in the statement of operations or as a component of
comprehensive income, depending on the type of hedging relationship that exists.
Statement No. 133 will be effective for fiscal years beginning after June 15,
1999. Conductus does not currently hold derivative instruments or engage in
hedging activities.

2.          ACCOUNTS RECEIVABLE:

            Accounts receivable, net, consists of the following:

<TABLE>
<CAPTION>
                                                                         MARCH 31,            DECEMBER 31,
                                                                           1999                  1998
                                                                   --------------------   --------------------
<S>                                                                <C>                    <C>
U.S. government contracts:
   Unbilled
      Recoverable costs and accrued profit on
         progress completed - not billed.........................   $        754,852       $       726,342
   Billed........................................................            371,726               297,525
Commercial.......................................................            245,682               378,562
Allowance for doubtful accounts..................................           (292,635)             (292,635)
                                                                   --------------------   --------------------
                                                                    $      1,079,625       $     1,109,794
                                                                   ====================   ====================
</TABLE>

                                     5
<PAGE>

                                 CONDUCTUS, INC.
               NOTES TO CONDENSED FINANCIAL STATEMENTS (CONTINUED)

                                   (Unaudited)

3.          INVENTORIES:

            Inventories, net, consist of the following:

<TABLE>
<CAPTION>
                                                                   MARCH 31,             DECEMBER 31,
                                                                      1999                   1998
                                                              --------------------   --------------------
<S>                                                           <C>                    <C>
Raw materials..............................................    $        548,893       $       441,130
Work in process............................................               3,935               198,341
Finished goods.............................................             591,384               640,666
Allowance for excess and obsolete inventories..............            (437,753)             (437,753)
                                                              --------------------   --------------------
                                                               $        706,459       $       842,384
                                                              ====================   ====================
</TABLE>

4.          LONG TERM DEBT:

            Our credit facilities consist of a loan from a leasing company, a
bank equipment term loan, a bank line of credit and a lease line of credit for
new equipment purchases. Obligations related to our credit facilities as of
March 31, 1999 and December 31, 1998 are as follows:

<TABLE>
<CAPTION>
                                                                    MARCH 31,             DECEMBER 31,
                                                                      1999                   1998
                                                              --------------------   --------------------
<S>                                                           <C>                    <C>
Loan payable to leasing company............................    $      1,828,468       $     1,978,366
Bank equipment term loan payable...........................             191,385               255,180
                                                              --------------------   --------------------
      Total................................................           2,019,853             2,233,546
Less: current portion......................................             854,050               892,139
                                                              --------------------   --------------------
      Long-term debt.......................................    $      1,165,803       $     1,341,407
                                                              ====================   ====================
</TABLE>

All of the credit facilities contain reporting and financial covenants. In the
event of default on any of these covenants, no further amounts would be advanced
to the Company under any facility. Additionally, the entire amounts outstanding
could become due and payable immediately upon default and those assets that are
collateralized could be seized, unless the lender waives such default. At March
31, 1999, Conductus was in compliance with all financial covenants.

5.          SUBSEQUENT EVENT:

            On May 4, 1999, the Company entered into a definitive agreement with
General Dynamics Information Systems, Inc. (GDIS) to license its high
temperature superconductive (HTS) electronics and cryoelectronics technology.
Under the license agreement, GDIS will purchase rights to Conductus' HTS
thin-film technology and other intellectual property for $5 million plus future
royalties and will have rights to use and sell this technology for use in U.S.
Government or state, local and foreign government markets, as defined. Under the
license agreement, GDIS made an immediate payment to the Company of $2,900,000.
In addition, GDIS will pay the Company $175,000 on the first day of each month
for 12 months beginning on July 1, 1999. The Company and GDIS also entered into
a Cross-License, Supply and Training Agreement under which the Company and GDIS
agreed to cross-license any updates to the licensed technology developed by
either party. Additionally, the Company will provide product and training to
GDIS in exchange for payment at standard commercial rates from GDIS.

                                     6
<PAGE>

                                 CONDUCTUS, INC.
               NOTES TO CONDENSED FINANCIAL STATEMENTS (CONTINUED)

                                   (Unaudited)

5.          SUBSEQUENT EVENT (CONTINUED):

            The following unaudited pro forma condensed balance sheet
information has been presented to give effect to the aforementioned transaction
as if it had occurred on March 31, 1999. The pro forma condensed balance sheet
information is presented for informational purposes only.

<TABLE>
<CAPTION>
                             Unaudited Pro Forma Condensed Balance Sheet
                                         (amounts in thousands)

                                                  March 31, 1999                                   March 31, 1999
                                                      Actual                    Adjustment            Pro Forma
                                                ------------------           ----------------    ------------------
<S>                                             <C>                          <C>                 <C>
ASSETS
Current assets:
Cash and cash equivalents                           $     989,625             $2,900,000 (1)         $   3,889,625
Short-term investments                                    557,727                                          557,727
Accounts receivable                                     1,079,625              2,100,000 (2)             3,179,625
Inventories                                               706,459                                          706,459
Prepaid expenses and other current assets                 117,161                                          117,161
                                                ------------------                               ------------------
Total current assets                                    3,450,597                                        8,450,597
Property and equipment, net                             1,815,877                                        1,815,877
Other assets                                                2,131                                           32,131
                                                ------------------                               ------------------
Total assets                                        $   5,298,605                                    $  10,298,605
                                                ==================                               ==================

LIABILITIES
Current liabilities:
Current portion of long-term debt                   $      54,050                                    $      54,050
Accounts payable                                          492,807                                          492,807
Other accrued liabilities                                 860,905                                          860,905
Total current liabilities                               2,207,762                                        2,207,762
Long-term debt, net of current portion                  1,165,803                                        1,165,803
                                                ------------------                               ------------------
Total liabilities                                       3,373,565                                        3,373,565
                                                ------------------                               ------------------

STOCKHOLDERS' EQUITY
Preferred stock                                         5,736,124                                        5,736,124
Common stock                                                  714                                              714
Additional paid-in-capital                             42,278,497                                       42,278,497
Accumulated deficit                                   (46,090,295)            $5,000,000 (1,2)         (41,090,295)
                                                ------------------                               ------------------
Total stockholders' equity                              1,925,040                                        6,925,040
                                                ------------------                               ------------------
Total liabilities and stockholders' equity          $   5,298,605                                    $  10,298,605
                                                ==================                               ==================
</TABLE>

(1)  The Company received a cash payment of $2,900,000 upon execution of the
     agreement, which has been reflected as cash.

(2)  The Company will receive 12 monthly cash payments of $175,000 beginning
     July 1, 1999, which have been reflected in accounts receivable.

                                     7
<PAGE>

Item 2 :  Management's Discussion and Analysis of Financial Condition and
Results of Operations

            THIS REPORT ON FORM 10-Q CONTAINS FORWARD-LOOKING STATEMENTS THAT
INVOLVE RISKS AND UNCERTAINTIES. CONDUCTUS, INC.'S (THE "COMPANY" OR
"CONDUCTUS") ACTUAL RESULTS MAY DIFFER MATERIALLY FROM THE RESULTS DISCUSSED IN
THE FORWARD-LOOKING STATEMENTS. FACTORS THAT MIGHT CAUSE SUCH A DIFFERENCE
INCLUDE, BUT ARE NOT LIMITED TO, THOSE DISCUSSED IN "RISK FACTORS" IN PART 1 OF
THE COMPANY'S ANNUAL REPORT ON FORM 10-K FOR THE YEAR ENDED DECEMBER 31, 1998.
THE FOLLOWING DISCUSSION SHOULD BE READ IN CONJUNCTION WITH THE FINANCIAL
STATEMENTS AND NOTES THERETO APPEARING ELSEWHERE IN THIS REPORT ON FORM 10-Q.

OVERVIEW

            We develop, manufacture and market electronic components and systems
based on superconductors for applications in the worldwide telecommunications
markets. As of March 31, 1999, we had accumulated losses of approximately
$46,090,000 and we expect to incur significant additional losses during the
remainder of 1999. We, alone or with collaborative partners, must successfully
develop, manufacture, introduce and market our potential products in order to
achieve profitability. We do not expect to recognize meaningful product sales
until we successfully develop and commercialize superconductive components,
systems and subsystems that address significant market needs.

RESULTS OF OPERATIONS FOR THE THREE MONTHS ENDED MARCH 31, 1999 AND 1998

            Total revenues consist primarily of contract revenue and, to a
lesser extent, product sales. Our total revenues increased by 17% to $1,314,000
for the quarter ended March 31, 1999 from $1,128,000 in the comparable period of
1998.

            Revenue under U.S. government research and development contracts
represented approximately 70% of total revenue for the quarter ended March 31,
1999 compared to 77% in the comparable period of 1998. Contract revenues
increased by 6% to $918,000 for the quarter ended March 31, 1999 from $864,000
in the comparable period of 1998. This increase is primarily attributable to the
growth of contract revenues related to our core wireless business. We have
submitted several proposals related to prospective contracts associated with
this core business and we will continue to submit proposals as additional
programs become available. We believe we will be able to participate in several
of the contracts for which proposals have been submitted and anticipate that
government contract revenues will continue to increase compared to 1998, however
we cannot assure you that we will receive the level of awards we anticipate.
Additionally, the recognition of revenue and receipt of payment pursuant to
these contracts and awards are subject to numerous risks.

            Product revenues increased by 50% to $397,000 from $264,000 in the
comparable period of 1998. The increase in product revenues was primarily the
result of an increase in sales of the Company's wireless telecommunications
products partially offset by a decrease in revenues from the sales of magnetic
sensing systems and other products which do not relate to our core market.

            Cost of product sales was primarily composed of costs of products
related to our wireless telecommunications products. Cost of product sales was
$570,000 for the period ended March 31, 1999 compared to $339,000 for the
comparable period of 1998. This increase is primarily attributable to the
increase in product sales and the lowered gross margins resulting from the
integration of the wireless products into the product mix during the comparison
periods.

            Research and development includes both externally and internally
funded projects. Research and development expenses were $1,121,000 in the
quarter ended March 31, 1999 compared to $2,298,000 in the comparable period of
the prior year. Research and development, as a percentage of revenue,
represented 85% and 204% in the quarters ended March 31, 1999 and 1998,
respectively. The decrease in research and development expense was primarily
attributable to a decrease in spending on internally funded projects partially
offset by an increase in spending on externally funded research and development
contracts. Although spending on internal research and development has decrease
from the prior year, we expect to continue to incur significant research and
development expenses on internally funded programs as we seek to develop
additional commercial products,

                                     8
<PAGE>

particularly in the wireless communications area and, as a result, anticipate
moderate increases in research and development expenses compared to the prior
year.

            Selling, general and administrative expenses include costs
associated with marketing, sales, and various administrative activities.
Selling, general and administrative expenses were $834,000 and $1,098,000 in the
quarters ended March 31, 1999 and 1998, respectively. The decrease in spending
was primarily due to decreases in sales, marketing and administrative headcount
compared to the prior year. Although selling, general and administrative
expenses decreased compared to the prior year, we expect sales and marketing
expenses to increase during 1999 to the extent we increase sales of commercial
products, particularly in the communications markets.

            Interest and other expense, net was $69,000 and $27,000 for the
periods ended March 31, 1999 and 1998, respectively. Interest charges related
primarily to our loan from a leasing company as well as our bank term loan. The
increase in interest expense was primarily the result of higher average debt
levels during the comparison periods.

            As a result of incurring losses, we have not incurred any income tax
liability. We have established a valuation allowance against our deferred tax
assets (principally the tax benefit of our net operating losses) and review this
allowance on a periodic basis. At such time that we believe that it is more
likely than not that the deferred tax asset will be realized, the valuation
allowance will be reduced.

            We do not believe that inflation has had a material effect on our
financial condition or results of operations during the past two fiscal years.
However, we cannot assure you that our business will not be affected by
inflation in the future.

LIQUIDITY AND CAPITAL RESOURCES

            We have financed our operations since inception primarily through:

            -  $13,251,000 in net proceeds from our initial public offering of
               common stock in August 1993.

            -  $9,892,000 in net proceeds from our follow-on public offering of
               common stock in June 1996,

            -  $20,989,000 raised in private placement financings,

            -  $44,888,000 from U.S. government contracts,

            -  $2,020,000 in outstanding borrowings under various lease and bank
               loan arrangements, and

            -  $3,810,000 in interest income.

            As of March 31, 1999 our aggregate cash, cash equivalents and short
term investments totaled $1,547,000. Additionally, we have a bank line of credit
facility and an equipment lease line. We may borrow up to a maximum of
$2,000,000 under the bank line of credit based on a limitation of 80% of certain
eligible receivables. As of March 31, 1999, the total amount outstanding under
the bank line of credit facility was $191,000 and no additional amount was
available under the line. Under the equipment lease, we may finance up to a
total of $1,000,000 of future equipment acquisitions. There were no balances
outstanding under the equipment line as of March 31, 1999.

            Net cash used in operations was $1,072,000 during the quarter ended
March 31, 1999. Net cash used in operations was primarily the result of the net
loss of $1,280,000 partially offset by the effect of a non-cash amortization
charge of $213,000 during the quarter. We anticipate that we will incur
significant additional net losses during 1999 and anticipate that our accounts
receivable and inventories may increase during 1999 as a result of increased
working capital requirements to support wireless telecommunications products. As
a result, we anticipate the use of additional cash in operating activities
during the remainder of 1999.

                                     9
<PAGE>

            Net cash provided by investing activities was $775,000 during the
quarter ended March 31, 1999. The balance was primarily related to the proceeds
from sales of short term investments during the quarter partially offset by
investments in additional property and equipment.

            Net cash used in financing activities was $261,000 during the
quarter ended March 31, 1999. This usage was primarily related to principal
payments under capital loans payable and equipment term loans as well as costs
to register the preferred stock issued in September of 1998.

            We anticipate total capital expenditures of approximately $900,000
during the remainder of 1999, which will be funded primarily from our $1,000,000
lease line of credit for new equipment purchases.

            All of our credit arrangements contain reporting and financial
covenants which we are required to satisfy. We cannot assure you that we will
satisfy all such covenants in the future. We cannot assure you that if we
default on any of the covenants, we could obtain a waiver of the default from
the lender. In the event of default on any of these covenants, no further
amounts would be advanced to us under any facility, the entire amounts
outstanding could become due and payable immediately upon default, and those
assets that are collateral could be seized, unless such default is waived by the
lender.

            To date we have received limited revenues from product sales. The
continued development of our products will require a commitment of substantial
funds to conduct further research and development and testing, to establish
commercial-scale manufacturing and to market these products. We expect to use
significant amounts of cash for capital equipment and to support operations
until product revenues increase. Additional financing may not be available on
acceptable terms or at all. Unless we are able to raise significant additional
funds, through debt or equity issuances, asset sales or otherwise, we will be
required to delay, reduce or eliminate one or more of our research and
development programs or obtain funds from collaborative partners or others that
may require us to relinquish rights to our technologies or potential products
that we would not otherwise relinquish. Our future capital requirements will
depend on many factors, including:

            -  continued progress in our research and development programs,

            -  the magnitude of these programs,

            -  the time and cost involved in obtaining any required regulatory
               approvals,

            -  the costs involved in preparing, filing, prosecuting, maintaining
               and enforcing patents,

            -  successful completion of technological, manufacturing and market
               requirements,

            -  changes in existing research relationships,

            -  the availability of funding under government contracts,

            -  our ability to establish collaborative arrangements, and

            -  the cost of manufacturing scale-up and the amount and timing of
               future revenues.

            As discussed in Note 5 of the Notes to Condensed Financial
Statements, the Company entered into a definitive agreement with General
Dynamics Information Systems, Inc. (GDIS) to license its high temperature
superconductive (HTS) electronics and cryoelectronics technology on May 4, 1999.
Under the license agreement, GDIS made an immediate payment to the Company of
$2,900,000. In addition, GDIS will pay the Company $175,000 on the first day of
each month for 12 months beginning on July 1, 1999.

            We anticipate that existing sources of liquidity and anticipated
revenue, primarily from government contracts in addition to the cash payments
resulting from the license transaction described above, will satisfy our
projected working capital and other cash requirements through Fiscal 1999.
However, there can be no assurance

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<PAGE>

that changes in our plans or other events affecting Conductus will not result
in the expenditure of our resources before then. Additionally, we can give you
no assurance that additional financing will be available on acceptable terms
or at all.

YEAR 2000 COMPLIANCE

            The potential problem presented by the year 2000 is the result of
computer programs being written using two digits rather than four to define the
applicable year. As a result, many computer systems and applications experience
problems handling dates beyond the year 1999 and will need to be modified before
the year 2000 in order to function properly. Any of our computer programs that
have date-sensitive software may recognize a date using "00" as the year 1900
rather than the year 2000. This could result in system failures or
miscalculations, causing disruptions of key operations. Important operations
which could be disrupted include, among other things, a temporary inability to
process transactions, send invoices, or engage in similar normal business
activities.

            We have expended resources to review our products, services and
internal use software to identify those products, services and systems that may
not properly process the year 2000 date. The costs related to potential year
2000 problems are expensed as incurred, and represent a reallocation of existing
resources.

            Our compliance project comprises four phases: (1) identification of
risks, (2) assessment of those risks, (3) development of remedies and
contingency plans, and (4) implementation and testing. The following describes
the status of our year 2000 compliance project, and our estimates regarding
future compliance expenses, in relation to four pertinent aspects of our
business:

            SALES, MANUFACTURING AND FINANCE INFORMATION SYSTEMS. We are
currently in the fourth phase of our compliance project. Our vendors have
confirmed that the versions of software currently in use are year 2000
compliant. We plan to complete our tests by the end of June 1999. We do not
anticipate incurring any material expenses to complete our tests on these
systems.

            NETWORK HARDWARE, SOFTWARE AND DESKTOP WORKSTATIONS. We have
completed phase three and have developed a plan to complete an upgrade of all
non-compliant hardware and software by June 1999. We estimate that we will spend
approximately $250,000 replacing non-compliant equipment.

            PRODUCTS WE HAVE SOLD. Our completed assessment indicates that these
products are year 2000 compliant. We do not anticipate incurring any material
expenses related to products we have sold or to any current product designs.

            FABRICATION AND MANUFACTURING EQUIPMENT. We are completing phase two
and beginning to develop remedies and contingency plans. We expect to complete
phase two by the end of March 1999, and to complete phase three by the end of
June 1999. We are unable to estimate the remaining financial impact, if any, of
the year 2000 because our assessment phase is not completed. However, we
currently anticipate that our $1,000,000 equipment lease line will be sufficient
to cover both the network costs and any costs that may be incurred related to
the upgrade or replacement of fabrication and manufacturing equipment in 1999.

            We have begun to formally communicate with our significant suppliers
and large customers to determine the extent to which we are vulnerable to their
failure to fix their own year 2000 problems. We cannot assure you that the
systems of other companies on which our systems rely will be timely converted,
or that a failure to convert by another company, or a conversion that is
incompatible with our systems, would not harm us.

            As our year 2000 compliance project continues, we may (a) discover
additional year 2000 problems, (b) may not be able to develop, implement, or
test remedies or contingency plans, or (c) may find that the costs of these
activities exceed current expectations and become material. These contingencies
could force us to spend additional time and money to avoid potential year 2000
problems.

            In the event we do not complete our compliance program as scheduled,
the year 2000 could cause significant problems. If all of our key operations
cease to function properly, we could experience an enterprise-wide

                                     11
<PAGE>

shutdown for an unknown period of time. We are unable to assess the magnitude
of any losses that could result from this worst case scenario.

Item 3:  Quantitative and Qualitative Disclosures About Market Risk

            Conductus' general policy is to limit the risk of principal loss and
ensure the safety of invested funds by limiting market and credit risk. Our
exposure to financial market risks relates primarily to our exposure to the
impact of changes in interest rates on our fixed income investment portfolio and
long-term debt obligations.

FIXED INCOME INVESTMENTS

            The primary objective of our investment activities is to preserve
our principal while maximizing yields without significantly increasing risk. To
achieve this objective, we maintain a portfolio that consists primarily of
short-term, high-quality commercial paper and foreign debt. All of our fixed
income investments have maturities of less than one year. Hence, our exposure
related to changes in interest rates is somewhat limited due to the short-term
nature of our portfolio. We do not use derivative financial instruments in our
investment portfolio.

DEBT OBLIGATIONS

            Conductus' outstanding debt consists of term loan obligations that
are primarily based on fixed rates. Therefore, our exposure to changes in
interest rates is limited because any increase or decrease in interest rates
would not significantly increase or decrease interest expense on our debt
obligations.

                                     12
<PAGE>

PART II:  OTHER INFORMATION

Item 1:  Legal Proceedings - Not Applicable

Item 2:  Changes in Securities - Not Applicable

Item 3:  Default upon Senior Securities - Not Applicable

Item 4:  Submission of Matters to a vote of Security Holders - Not Applicable

Item 5:  Other Information

            Holders of our common stock currently enjoy the substantial benefit
of being able to easily buy or sell our common stock because our common stock is
listed on the Nasdaq SmallCap Market trading system. In November 1998, Nasdaq
informed us that, on the basis of our Quarterly Report on Form 10-Q for the
quarter ending September 30, 1998, our net tangible assets had fallen below the
level required for continued listing of our common stock on the Nasdaq National
Market trading system. Subsequently, we submitted information to Nasdaq
regarding our anticipated future net tangible assets and certain financing
plans. Based on this submission, we applied to have our common stock listed on
the Nasdaq SmallCap Market. Pending approval of our application, our common
stock began trading on the Nasdaq SmallCap Market. Nasdaq informed us that 
our application to be listed on the Nasdaq SmallCap Market has been denied. 
We requested an oral hearing on the subject which was held on May 13, 1999, 
and delisting of our common stock has been stayed pending the results of this 
hearing.

            Although we satisfied Nasdaq's requirements for listing on the 
Nasdaq SmallCap Market as of December 31, 1998, we did not satisfy these 
requirements as of March 31, 1999. As a result of our recent license 
agreement with General Dynamics, we believe we have taken sufficient action 
to bring us within compliance of the listing requirements. We are also 
seeking to raise additional equity capital and reduce our operating losses. 
However, we may not be successful in these efforts. In addition, even if we 
are now compliant with Nasdaq's listing requirements, Nasdaq may deny our 
appeal if they believe we will not satisfy the criteria over the longer term.

            If our common stock is delisted, trading in our common stock, if
any, would then be conducted in the over-the-counter market on an electronic
bulletin board, or in what are commonly referred to as the "pink sheets."
Stockholders would then find it more difficult to sell, or to quickly and
accurately obtain quotations as to the price of, our common stock.

            In addition, if we fail to maintain either (a) net tangible assets,
as defined in Rule 3a51-1 of the Securities Exchange Act, of at least $2,000,000
or (b) average revenue over a three year period of at least $6,000,000, we could
become subject to certain "penny stock" rules. These rules subject brokers and
dealers who sell or make a market in our common stock to additional trading
rules and requirements. For example, these brokers or dealers would be required
to maintain detailed records on Conductus and their own trading activities in
connection with our common stock. Consequently, this could affect the
willingness of brokers and dealers to sell or make a market in our common stock.
This, in turn, could affect stockholder's ability to quickly and easily sell our
common stock.

                                     13
<PAGE>

Item 6:  Exhibits and Reports on Form 8-K

(A)  Exhibits

                                  EXHIBIT INDEX

       EXHIBIT
         NO.                       DESCRIPTION
------------------------ ------------------------------------------------------

         2.1(1)           Stock Exchange Agreement dated as of May 28, 1993,
                          between the Company and Tristan Technologies, Inc.

         3.1(2)           Restated Certificate of Incorporation.

         3.2(3)           Restated Bylaws.

         3.3(4)           Certificate of Designation of Series B Preferred
                          Stock.

         4.1(3)           Stockholder Rights Plan.

        10.1(1)           1987 Stock Option Plan.

        10.2(1)           Amended 1989 Stock Option Plan.

        10.3(5)           1992 Stock Option/Stock Purchase Plan.

        10.4(6)           1994 Employee Stock Purchase Plan.

        10.5(1)           Second Amended and Restated Registration Rights
                          Agreement dated June 3, 1993.

        10.6(4)           Form of Series B Preferred Stock and Warrant Purchase
                          Agreement, dated September, 1998, and September 22,
                          1998, between the Company and the Series B Investors.

        10.7(4)           Form of Warrant to Purchase Common Stock between the
                          Company and the Series B Investors.

        10.8(7)           Employment Agreement dated May 3, 1994 between
                          Registrant and Mr. Charles E. Shalvoy.

        10.9(1)           Form of Indemnification Agreement between the
                          Registrant and each of its directors and officers.

        10.10(1)+         Coordinated Research Program Agreement dated October
                          14, 1988 and Amendment dated May 26, 1991 between the
                          Registrant and Hewlett-Packard Company ("H-P"), as
                          amended by the Agreement between Registrant and
                          Hewlett-Packard Company dated June 2, 1993.

        10.11(8)          Collaboration Agreement between Registrant and CTI
                          dated September 19, 1995.

        10.12(8)          High Temperature Superconductor Thin-Film
                          Manufacturing Alliance Agreement among Registrant,
                          Superconductor Technologies, Inc., Stanford
                          University, Georgia Research Corporation,
                          Microelectronic Control and Sensing Incorporated,
                          IBIS, Focused Research and BDM Federal dated November
                          17, 1995.

        10.13(9)+         Superconducting Filter Technology Joint Development
                          Agreement dated April 25, 1996 between the Registrant
                          and Lucent Technologies Inc.

        10.14(4)          Engagement Letter between the Company and Sutro and
                          Co. Inc., dated March 24, 1998.

        10.15(4)          Amendment to Engagement Letter between the Company and
                          Sutro and Co. Inc., dated September 2, 1998.

        10.16(4)          Engagement Letter between the Company and Davenport
                          and Co., dated September 2, 1998.

        10.17(4)          Master Lease Agreement between the Company and Leasing
                          Technologies International, Inc., dated June 15, 1998.

        10.18(1)          Lease Agreement dated May 3, 1993 between the
                          Registrant and Mozart-McKee Limited Partnership for
                          Sunnyvale facilities.

        10.19(7)          Lease Agreement dated December 8, 1994 between
                          Registrant and Mozart-McKee Limited Partnership for
                          Sunnyvale facilities.

        10.20(7)          Business Loan Agreement dated August 15, 1994 between
                          Registrant and Silicon Valley Bank for working capital
                          credit facility and term loan facility.

        10.21(10)         Loan Modification Agreement dated June 30, 1997,
                          between Registration and Silicon Valley Bank modifying
                          the Business Loan Agreement dated August 15, 1994.

        10.22(10)         Loan Modification Agreement dated November 12, 1997,
                          between Registration and Silicon Valley Bank modifying
                          the Business Loan Agreement dated August 15, 1994.

        10.23(10)         Loan Modification Agreement dated December 23, 1997,
                          between Registration and Silicon Valley Bank modifying
                          the Business Loan Agreement dated August 15, 1994.

        10.24(11)         Business Loan Agreement dated March 8, 1996 between
                          Registrant and Silicon Valley Bank for working capital
                          credit facility and term loan facility.

                                     14
<PAGE>

        10.25(12)         Business Loan Agreement dated December 27, 1996
                          between Registrant and Silicon Valley Bank for working
                          capital credit facility and term loan facility.

        10.26(4)          Master Loan and Security Agreement between the Company
                          and Transamerica Business Credit Corporation, dated
                          June 26, 1998.

        10.27(4)          Stock Subscription Warrant Agreement between the
                          Company and Transamerica Business Credit Corporation,
                          dated June 26, 1998.

        10.28(13)         Silicon Valley Bank Loan Agreement.

        10.29(13)         Collateral Assignment, Patent Mortgage and Security
                          Agreement between the Company and Silicon Valley Bank.

        10.30(10)+        Asset Purchase Agreement dated July 9, 1997 between
                          Registrant and Bruker Instruments, Inc. for sale of
                          assets of Registrant's NMR Probe business.

        10.31(10)         Asset Purchase Agreement dated August 15, 1997 between
                          Registrant and Neocera, Inc. for sale of Registrant's
                          assets related to its temperature controller business.

        10.32(10)         Asset Purchase Agreement dated September 3, 1997,
                          between Registrant and Niki Glass Ltd. for sale of
                          Registrant's assets related to portions of its
                          instruments business.

        10.33             License Agreement with General Dynamics, dated May 4,
                          1999.

        10.34             Cross-License, Supply and Training Agreement, dated
                          May 4, 1999.

        27.1              Financial Data Schedule.

+         Confidential treatment granted or requested as to certain portions of
          these exhibits.

(1)       Incorporated herein by reference to the Company's Registration
          Statement on Form S-1 (Number 33-64020), filed with the SEC on May 15,
          1996, as amended.

(2)       Incorporated herein by reference to the Company's 1993 Annual Report
          on Form 10-K.

(3)       Incorporated herein by reference to the Company's Registration
          Statement on Form 8-K filed with the SEC on January 22, 1998.

(4)       Incorporated herein by reference to the Company's Form 10-Q, filed
          with the SEC on November 16, 1998.

(5)       Incorporated herein by reference to the Company's Registration
          Statement on Form S-8, filed with the SEC on November 26, 1997.

(6)       Incorporated herein by reference to the Company's Registration
          Statement on Form S-8, filed with the SEC on August 5, 1994.

(7)       Incorporated herein by reference to the Company's 1994 Annual Report
          on Form 10-K.

(8)       Incorporated herein by reference to Amendment No. 2 to the Company's
          Registration Statement on Form S-1 (Number 333-3815), filed with the
          SEC on June 17, 1996.

(9)       Incorporated herein by reference to the Company's Registration
          Statement on Form S-1 (Number 333-3815), filed with the SEC on May 10,
          1996, as amended.

(10)      Incorporated herein by reference to the Company's 1998 Annual Report
          on Form 10-K.

(11)      Incorporated herein by reference to the Company's 1995 Annual Report
          on Form 10-K.

(12)      Incorporated herein by reference to the Company's 1996 Annual Report
          on Form 10-K.

(13)      Incorporated herein by reference to the Company's Form 10-Q, filed
          with the SEC on May 14, 1998.

(B) Reports on Form 8-K.

The Company filed no reports on Form 8-K during the quarter for which this
report is filed.

                                     15
<PAGE>

SIGNATURES

            Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                             CONDUCTUS, INC.

Dated:  May 17, 1999         /s/ Ron Wilderink
                             ----------------------------------------------
                             Ron Wilderink, Vice President of Finance
                             and Chief Financial Officer

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