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                                                                   Exhibit 10.31

                      SUPPLEMENTAL STOCKHOLDERS' AGREEMENT

     This Supplemental Stockholders' Agreement (this "Agreement"), dated as of
March __, 2001, by and among Tellium, Inc., a Delaware corporation (the
"Company"), and the parties hereto listed in Schedule I hereto (the "Holders").

     WHEREAS, the Holders collectively were granted options to purchase 650,000
shares (the "Private Shares") of the Company's common stock, par value $.001 per
share (the "Common Stock"), pursuant to Option Agreements between the Company
and the Holders dated as of the date hereof (the "Option Agreements") in
connection with their service on the Company's advisory board; and

     WHEREAS, in connection with the foregoing, the Company has agreed to grant
certain rights with respect to the Registrable Shares.

     NOW, THEREFORE, in consideration of these premises and the mutual
agreements, provisions and covenants contained in this Agreement, the parties
hereby agree as follows:

     1. Certain Definitions
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        As used in this Agreement, the following terms shall have the meanings
set forth below:

     "Common Stock" means the Common Stock, as such phrase is defined in the
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recitals to this Agreement.

     "Holders" means the parties hereto listed in Schedule I hereto.
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     "Person" means any individual, corporation, limited liability company,
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limited or general partnership, joint venture, association, joint-stock company,
trust, unincorporated organization or government or any agency or political
subdivisions thereof.

     "Private Shares" means the Private Shares as such phrase is defined in the
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recitals to this Agreement; provided, however, that Private Shares shall cease
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to be Private Shares (x) upon their sale pursuant to a registration statement or
Rule 144 under the Securities Act, (y) upon their sale pursuant to Rule 144
under the Securities Act or (z) upon their sale in any manner to a Person which
is not entitled to the rights provided by this Agreement.

     "Rule 144" means Rule 144 promulgated under the Securities Act or any
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successor rule thereto or any complementary rule thereto.
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     "Securities Act" means the Securities Act of 1933, as amended, and the
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rules and regulations of the Commission thereunder, all as the same shall be in
effect from time to time.

     2. Holders' Agreements. Each Holder agrees that it will not transfer any
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Registrable Shares without complying with Section 13 of the Option Agreements.

     3. Registration Rights
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        3.1 General. Subject to Section 3.2, and in respect of their Private
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Shares, the parties to this Agreement shall be considered "Holders" pursuant to
Section 1.5(c) of the Amended and Restated Stockholders Agreement by and among
the Company and the other parties thereto dated as of September 19, 2000 (as
amended from time to time) (the "Current Stockholders Agreement") with respect
to any Demand Registration, Piggyback Registration or S-3 Registration and with
respect to the Shelf Registration Statement (as each such term is defined in the
Current Stockholders Agreement), shall be accorded the rights, in respect of
Article VII, to which such "Holders" are entitled under Section 8.5 of the
Current Stockholders Agreement, and agree to the obligations and other duties to
which such "Holders" have agreed under Article VII (and, in respect to Article
VII, under Section 8.5) of the Current Stockholders Agreement. Any permitted
assign of a party to this Agreement shall agree to this Section 3 prior to being
accorded the rights hereunder.

        3.2 Application. A Holder (as such term is defined in this Agreement)
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(i) shall not be entitled to the right to demand set forth in Section 7.2(a)(ii)
of the Current Stockholders Agreement, (ii) shall not be entitled to vote or
consent in respect of adding one or more Persons to the Current Stockholders
Agreement, and (iii) shall be subject to the 90 day period related to holders of
the Company's Series E Preferred Stock (in lieu of the 180 day period)
referenced in Section 7.4 of the current Stockholders Agreement, without regard
to whether such Holder sells under the Shelf Registration Statement or
otherwise.

     4. Miscellaneous Provisions
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        4.1 Specific Performance, Etc. The Company and each Holder, in addition
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to being entitled to exercise all rights provided herein, in the Company's
Amended and Restated Certificate of Incorporation or granted by law, including
recovery of damages, shall be entitled to specific performance of its rights
under this Agreement. Each party agrees that monetary damages would not be
adequate compensation for any loss incurred by reason of a breach by it of the
provisions of this Agreement and hereby agrees to waive the defense in any
action for specific performance that a remedy at law would be adequate.

        4.2 Notices. All notices, requests, demands and other communications
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which are required or may be given under this Agreement shall be in writing and
shall be deemed to have been duly given and received in accordance with the
applicable provision of the Stock Purchase Agreement to which a Holder is a
party.

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        4.3 Entire Agreement; Amendments and Waivers. This Agreement constitutes
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the entire agreement among the parties pertaining to the subject matter hereof
and supersedes all prior agreements, understandings, negotiations and
discussions, whether oral or written, of the parties hereto. The provisions of
this Agreement, including the provisions of this sentence, may not be amended,
modified or supplemented, and waivers of or consents to departures from the
provisions hereof may not be given unless approved in writing by the Company and
Holders of at least 50% of the Registrable Shares. No action taken pursuant to
this Agreement, including, without limitation, any investigation by or on behalf
of any party, shall be deemed to constitute a waiver by the party taking such
action. The waiver by any party hereto of a breach of any provision of this
Agreement shall not operate or be construed as waiver of any preceding or
succeeding breach and no failure by any party to exercise any right or privilege
hereunder shall be deemed a waiver of such party's rights or privileges
hereunder or shall be deemed a waiver of such party's rights to exercise the
same at any subsequent time or times hereunder.

        4.4 Termination. If not terminated sooner pursuant to the terms hereof,
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Section 3 of this Agreement (regarding registration rights) shall terminate and
cease to be of any further force or effect upon the Company's merger with and
into another corporation, or another corporation's merger with and into the
Company, where, in connection with the merger, the Registrable Shares are
exchanged exclusively for cash and/or shares of capital stock or other
securities that are registered under the Securities Act and publicly traded on a
national securities exchange or authorized for trading on the Nasdaq National
Market System.

        4.5 Recapitalizations, Exchange, etc. Affecting the Company's Stock. The
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provisions of this Agreement shall apply, to the full extent set forth herein
with respect to the Registrable Shares, to any and all shares of capital stock
of the Company that may be issued in respect of, in exchange for, or in
substitution of the Registrable Shares and shall be appropriately adjusted for
any stock dividends, splits, reverse splits, combinations, recapitalizations and
the like occurring after the date hereof.

        4.6 Multiple Counterparts. This Agreement may be executed any number of
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counterparts, and each such counterpart shall be deemed an original instrument,
but all such counterparts shall constitute but one agreement.

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

        4.8 Governing Law. This Agreement shall be governed by and construed in
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accordance with the internal laws of the State of New York, without regard to
principles of conflict of laws thereof.

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         IN WITNESS WHEREOF, the undersigned have executed this Agreement as of
the date set forth above.

                            TELLIUM, INC.


                            By:
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                                Name:
                                Title:

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