Document:

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                                                                   EXHIBIT 10.32

                               SECURITY AGREEMENT

      THIS AGREEMENT, entered into as of December 28, 2000, between Conductus,
Inc., a Delaware corporation (the "Company"), and Charles E. Shalvoy (the
"Purchaser"),

                              W I T N E S S E T H:

      WHEREAS, the Purchaser has purchased from the Company 135,301 shares of
the Company's Common Stock (the "Shares"); and

      WHEREAS, the Company has loaned to the Purchaser the sum of $460,244.25
which the Purchaser has used to pay the purchase price of the Shares; and

      WHEREAS, the Purchaser has executed and delivered to the Company a
full-recourse promissory note evidencing such loan (the "Note") and has agreed
to pledge all of the Shares to the Company as security for the payment of the
Note:

      NOW, THEREFORE, it is agreed as follows:

      1. The Purchaser hereby delivers to the Company one or more certificates
representing the Shares, together with two Assignments Separate From Certificate
signed by the Purchaser. The Purchaser hereby pledges and grants a security
interest in the Shares, including any shares into which the Shares may be
converted and all proceeds of the Shares, as security for the timely payment of
all of the Purchaser's obligations under the Note and for the Purchaser's
performance of all of its obligations under this Agreement. In the event of a
default in payment of the Note, the Purchaser hereby appoints the Company as his
true and lawful attorney to take such action as may be necessary or appropriate
to cause the Shares to be transferred into the name of the Company or any
assignee of the Company and to take any other action on behalf of the Purchaser
permitted hereunder or under applicable law.

      2. The Company agrees to hold the Shares as security for the timely
payment of all of the Purchaser's obligations under the Note and for the
Purchaser's performance of all of its obligations under this Agreement, as
provided herein. At no time shall the Company dispose of or encumber the Shares,
except as otherwise provided in this Agreement.

      3. At all times while the Company is holding the Shares as security under
this Agreement, the Company shall:

            (a) Collect any dividends that may be declared on the Shares and
      credit such dividends against any accrued interest or unpaid principal
      under the Note, as part payment;

            (b) Collect and hold any shares that may be issued upon conversion
      of the Shares; and

            (c) Collect and hold any other securities or other property that may
      be distributed with respect to the Shares.

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Such shares and other securities or property shall be subject to the security
interest granted in Section 1 of this Agreement and shall be held by the Company
under this Agreement.

      4. While the Company holds the Shares as security under this Agreement,
the Purchaser shall have the right to vote the Shares at all meetings of the
Company's shareholders; provided that the Purchaser is not in default in the
performance of any term of this Agreement or in any payment due under the Note.
In the event of such a default, the Company shall have the right to the extent
permitted by law to vote and to give consents, ratifications and waivers and
take any other action with respect to the Shares with the same force and effect
as if the Company were the absolute and sole owner of the Shares.

      5. Upon payment in full of the outstanding principal balance of the Note
and all interest and other charges due under the Note, the Company shall release
from pledge and redeliver to the Purchaser the certificate(s) representing the
Shares and the Assignment Separate From Certificate forms, provided all rights
of repurchase under the terms of the stock option grant shall have elapsed.

      6. In the event that the Purchaser fails to perform any term of this
Agreement or fails to make any payment when due under the Note, the Company
shall have all of the rights and remedies of a creditor and secured party at law
and in equity, including (without limitation) the rights and remedies provided
under the Uniform Commercial Code.

            Without limiting the foregoing, the Company may, after giving ten
(10) days' prior written notice to the Purchaser by certified mail at his
residence or business address, sell any or all of the Shares in such manner and
for such price as the Company may determine, including (without limitation)
through a public or private sale or at any broker's board or on any securities
exchange, for cash, upon credit or for future delivery. The Company is
authorized at any such sale, if it deems it advisable to do so, to restrict the
prospective bidders or purchasers of any of the Shares to persons who will
represent and agree that they are purchasing for their own account for
investment, and not with a view to the distribution or sale of any of the
Shares, to restrict the prospective bidders or purchasers and the use any
purchaser may make of the Shares and impose any other restriction or condition
that the Company deems necessary or advisable under the federal and state
securities laws.

            Upon any such sale the Company shall have the right to deliver,
assign and transfer to the purchaser thereof the Shares so sold. Each purchaser
at any such sale shall hold the Shares so sold absolute, free from any claim or
right of any kind. In case of any sale of any or all of the Shares on credit or
for future delivery, the Shares so sold may be retained by the Company until the
selling price is paid by the purchaser thereof, but the Company shall not incur
any liability in case of the failure of such purchaser to take up and pay for
the Shares so sold and, in case of any such failure, such Shares may again be
sold under the terms of this section.

            The Purchaser hereby agrees that any disposition of any or all of
the Shares by way of a private placement or other method which in the opinion of
the Company is required or advisable under Federal and state securities laws is
commercially reasonable. At any public sale, the Company may (if it is the
highest bidder) purchase all or any part of the Shares at such price as the
Company deems proper. Out of the proceeds of any sale, the Company may retain an

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amount sufficient to pay all amounts then due under the Note, together with the
expenses of the sale and reasonable attorneys' fees. The Company shall pay the
balance of such proceeds, if any, to the Purchaser. The Purchaser shall be
liable for any deficiency that remains after the Company has exercised its
rights under this Agreement.

      7. This Agreement shall be governed by and construed in accordance with
the laws of the State of California without regard to choice of law provisions.

            This Agreement shall inure to the benefit of, and be binding upon,
the Company and its successors and assigns and be binding upon the purchaser and
the Purchaser's legal representative, heirs, legatees, distributees, assigns and
transferees by operation of law.

            This Agreement contains the entire security agreement between the
Company and the Purchaser.

            The Purchaser will execute any additional agreements, assignments or
documents or take any other actions reasonably required by the Company to
preserve and perfect the security interest in the Shares granted to the Company
herein and otherwise to effectuate this Agreement.

      IN WITNESS WHEREOF, the Company has caused this Agreement to be executed
on its behalf by its duly authorized officer, and the Purchaser has personally
executed this Agreement.

                                        Conductus, Inc.

                                        By
                                           ------------------------------------
                                        Title
                                              ---------------------------------

                                        ---------------------------------------
                                                       Purchaser<PAGE>

                                                                   EXHIBIT 10.33

                          FULL-RECOURSE PROMISSORY NOTE

$360,000                                                   Sunnyvale, California

                                                      Dated as of August 21 2001

      FOR VALUE RECEIVED, the undersigned, Charles E. Shalvoy, promises to pay
to the order of Conductus, Inc., a Delaware corporation (the "Company"), the
principal sum of three hundred sixty thousand dollars ($360,000.00) with
interest from the date hereof on the unpaid principal as specified herein. The
entire unpaid balance of principal and interest shall be due and payable on the
earlier to occur of (l) August 22, 2006, or (2) termination of employment with
the Company. Notwithstanding the foregoing, the Company shall have the right to
demand full payment of the unpaid principal and interest thereon at anytime upon
fifteen (15) days prior written notice.

      The interest rate on this note shall be an annual rate of interest equal
to four and ninety-nine- hundredths percent (4.99%). Interest shall be computed
on the basis of a year of 365 days and the actual number of days elapsed, except
that interest shall not be computed on the day of full repayment of this note.
Interest not paid when due shall earn interest at the rate specified above.

      If payment is not made when due, and if action is instituted on this note,
the undersigned agrees to pay the Company reasonable attorneys' fees and costs
of suit, as fixed by court.

      The undersigned shall have the right to prepay all or any part of the
unpaid principal amount of this note, without premium, at any time prior to the
maturity hereof.

                                       -1-
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      This note is a full-recourse note originally secured by a pledge of shares
of Common Stock of the Company pursuant to a Security Agreement of even date
herewith, which is on file with the Secretary of the Company.

      This note shall be governed by and construed in accordance with the laws
of the State of California without regard to California choice of law
provisions.

      IN WITNESS WHEREOF, the undersigned has signed, dated and delivered this
note as of the date and year first above written.

                                             -----------------------------------
                                                          Signature

                                       -2-

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