<PAGE>

                                                                    EXHIBIT 4.02

                          INVESTORS' RIGHTS AGREEMENT

     This Investors' Rights Agreement (this "Agreement") is made and entered
into as of May 1, 2000 by and among ONI Systems Corp., a Delaware
corporation (the "Company"), which succeeded its California predecessor, Optical
Networks, Incorporated, upon reincorporation in Delaware, and assumed the
Investors' Rights Agreement of Optical Networks, Incorporated, dated December
22, 1999 (the "Prior Rights Agreement"), with its principal office at 166
Baypointe Parkway, San Jose, California 95134, the persons and entities listed
on Exhibit A attached hereto (the "Investors"), Venture Lending & Leasing, Inc.
("VLLI"), COLT Telecom plc ("COLT"), Fenwick & West LLP ("F&W"), FMR Corp.
("FMR") and Internet Initiative Japan Inc. ("IIJ").

                                R E C I T A L S
                                - - - - - - - -

     A.   Certain of the Investors (the "Series B and C Investors") are holders
of outstanding shares of the Company's Series B Preferred Stock ("Series B
Stock") and Series C Preferred Stock ("Series C Stock") issued by the Company to
such Investors pursuant to that certain Series B and C Preferred Stock Purchase
Agreement by and among the Company and such Investors dated December 19, 1997
(the "Series B and C Agreement"), and have been granted certain information
rights, registration rights and rights of first refusal under the Prior Rights
Agreement of the Company.

     B.   Certain of the Investors (the "Additional Series C Investors") are
holders of outstanding shares of the Series C Stock issued by the Company to
such Additional Series C Investors pursuant to that certain Series C Preferred
Stock Purchase Agreement by and among the Company and the Additional Series C
Investors dated March 10, 1998 (the "Additional Series C Agreement"), and have
also been granted certain information rights, registration rights and rights of
first refusal under the Prior Rights Agreement.

     C.   VLLI holds certain warrants (the "VLLI Warrants") to acquire up to an
aggregate of 175,101 shares of common stock of Optivision, Inc. ("Optivision")
and pursuant to the terms of Section 8 thereof was promised certain registration
rights (identical to those granted by Optivision to ADC Telecommunications,
Inc.) with respect to the shares issuable thereunder. Pursuant to Section 4.2(c)
of the VLLI Warrants, VLLI is entitled, upon exercise of the VLLI Warrants in
accordance with their terms, to receive up to 233,468 shares (such number as
adjusted to reflect the one-for-three reverse split of the Common Stock of the
Company effected on March 11, 1998 and the two-for-one forward split of the
Common Stock of the Company effected on August 13, 1999) of the Common Stock of
the Company (the "VLLI Common Shares"). Pursuant to Section 1.2 of that certain
Contribution, Services and Share Purchase Agreement dated October 29, 1997
between Optivision and the Company, the Company has reserved such number of
shares of its Common Stock for issuance upon the exercise of the VLLI Warrants.
The Company has granted VLLI registration rights with respect to such shares of
Common Stock under the terms of the Prior Rights Agreement.

     D.   Cisco Systems, Inc. ("Cisco" or the "Series D Investor") is a holder
of outstanding shares of the Company's Series D Preferred Stock ("Series D
Stock") issued by the Company pursuant to that certain Series D Preferred Stock
Purchase Agreement by and between the Company and Cisco

                                      -1-
<PAGE>

dated April 1, 1998 (the "Series D Agreement") and has also been granted certain
information rights, registration rights and rights of first refusal under the
Prior Rights Agreement.

     E.   Certain Investors (the "Series E Investors") are holders of
outstanding shares of the Company's Series E Preferred Stock ("Series E Stock")
issued by the Company pursuant to that certain Series E Preferred Stock Purchase
Agreement by and among the Company and the Series E Investors dated December 23,
1998 (the "Series E Agreement") and have also been granted certain information
rights, registration rights and rights of first refusal under the Prior Rights
Agreement.

     F.   Certain Investors (the "Series F Investors") are holders of
outstanding shares of the Company's Series F Preferred Stock ("Series F Stock")
issued by the Company pursuant to that certain Series F Preferred Stock Purchase
Agreement by and among the Company and the Series F Investors dated September 2,
1999 (the "Series F Agreement") and have also been granted certain information
rights, registration rights and rights of first refusal under the Prior Rights
Agreement.

     G.   COLT holds a warrant to purchase up to an aggregate of 500,000 shares
of Common Stock of the Company, pursuant to the Warrant to Purchase Common Stock
of Optical Networks, Incorporated, dated December 8, 1999, between COLT and the
Company (the "COLT Warrant"). Under Section 4.5 of the COLT Warrant, the Company
agreed to grant to COLT the registration rights granted to it under this
Agreement. The common stock issuable to COLT under the COLT Warrant are
hereinafter referred to as the "COLT Common Shares."

     H.   Certain Investors (the "Series G Investors") are holders of
outstanding shares of the Company's Series G Preferred Stock ("Series G Stock")
issued by the Company pursuant to that certain Series G Preferred Stock Purchase
Agreement by and among the Company and the Series G Investors dated December 22,
1999 (the "Series G Agreement") and have also been granted certain information
rights, registration rights and rights of first refusal under the Prior Rights
Agreement.

     I.   FMR holds a warrant to acquire up to an aggregate of 200,000 shares of
Common Stock of the Company, pursuant to the Warrant to Purchase Common Stock of
Optical Networks, Incorporated, dated February 15, 2000, between FMR and the
Company (the "FMR Warrant"). The common stock issuable to FMR under the FMR
Warrant are hereinafter referred to as the "FMR Common Shares."

     J.   F&W holds a warrant to acquire up to an aggregate of 200,000 shares of
Common Stock of the Company, pursuant to the Warrant to Purchase Common Stock of
Optical Networks, Incorporated, dated March 9, 2000, between F&W and the Company
(the "F&W Warrant"). Under Section 7 of the F&W Warrant, the Company agreed to
grant to F&W the registration rights granted to it under this Agreement. The
common stock issuable to F&W under the F&W Warrant are hereinafter referred to
as the "F&W Common Shares."

     K.   Pursuant to the Subscription Agreement, dated March 27, 2000, between
IIJ and the Company (the "Subscription Agreement"), IIJ has agreed to purchase
concurrently with the Company's initial public offering, the number of shares
Common Stock of the Company equal to $4,000,000 divided by the per share price
to the public in the Company's initial public offering. Pursuant to Section 3 of
the Subscription Agreement, the Company agreed to grant to IIJ the registration
rights granted to it under this Agreement. The Series B and C Investors,
Additional Series C Investors, Series

                                      -2-
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D Investor, Series E Investors, Series F Investors Series G Investors and VLLI
are collectively referred to herein as the "Prior Investors."

     L.   Certain Investors (the "Series H Investors") have agreed to purchase
shares of the Company's Series H Preferred Stock ("Series H Stock") pursuant to
a certain Series H Preferred Stock Purchase Agreement dated of even date
herewith (the "Series H Agreement"). The Series H Agreement provides that, as a
condition to the Series H Investors purchase of Series H Stock thereunder, the
Series H Investors will be granted the rights set forth herein.

     N.   The Company and the undersigned parties hereto desire to enter into
this Agreement in order to amend, restate and replace their rights and
obligations under the Prior Rights Agreement with the rights and obligations set
forth in this Agreement.  Section 4.3 of the Prior Rights Agreement provides
that the Prior Rights Agreement may be amended by the written consent of the
holders of a majority of the "Registrable Securities" (as defined in the Prior
Rights Agreement) and the undersigned parties to this Agreement hold a majority
of the Registrable Securities.

     NOW, THEREFORE, in consideration of the foregoing recitals and the mutual
promises hereinafter set forth, the parties hereto agree as follows:

     1.   INFORMATION RIGHTS.
          ------------------

     The Company hereby covenants as follows:

          1.1  Financial Information.  The Company shall furnish the following
reports to each Investor and/or its assignee or transferee for so long as such
Investor, assignee, or transferee is the record holder of any of the Securities
(as defined in Section 2.1 below):

          (i)  As soon as practicable after the end of each fiscal quarter
(except the fourth quarter), and in any event within 45 days thereafter, an
unaudited income statement for such fiscal quarter and an unaudited balance
sheet as of the end of such fiscal quarter.

          (ii) As soon as practicable after the end of each fiscal year, and in
any event within 90 days thereafter, an income statement for such fiscal year, a
balance sheet of the Company as of the end of such fiscal year, a statement of
stockholder's equity as of the end of such fiscal year, and a statement of
changes in financial condition for such fiscal year, all certified by
independent public accountants of recognized national standing selected by the
Company.

All financial statements provided for above shall be prepared in accordance with
generally accepted accounting principles applied on a consistent basis (except
that such unaudited financial statements may be prepared without footnotes and
will be subject to normal year-end audit adjustments).

          1.2  Additional Financial Information.  The Company shall furnish to
each Investor, so long as such Investor is the record holder of at least 15% of
the aggregate Securities originally purchased under the Series B and C
Agreement, Additional Series C Agreement, Series D Agreement, Series E
Agreement, Series F Agreement, Series G Agreement or Series H Agreement, as
applicable, such financial reports of the Company as are provided to the
Company's Board of Directors (the

                                      -3-
<PAGE>

"Board") as promptly as possible upon their provision to the Board. Any
information obtained by such Investor pursuant to this Section 1.2 which may be
proprietary to the Company or otherwise confidential will not be disclosed
without the prior written consent of the Company. Information so obtained which
may be considered "inside" non-public information will not be utilized by such
Investor in connection with purchases and/or sales of the Company's securities
except in compliance with applicable state and federal antifraud statutes.

          1.3  Termination of Financial Information Rights.  The Company's
obligation to deliver the financial statements under Sections 1.1 and 1.2 shall
terminate and shall be of no further force or effect when a public market first
exists for any of the Company's securities.  Thereafter, the Company shall
deliver to each Investor, and its assignee or transferee, such financial
information as the Company from time to time provides to holders of its Common
Stock.

          1.4  Board Representation.  The parties shall vote their shares of
stock of the Company so as to elect the Chief Executive Officer of the Company
as one of the two directors to be elected to the Board by the holders of record
of the Preferred Stock and the Common Stock, voting together as a single class,
pursuant to the Company's Amended and Restated Certificate of Incorporation (the
"Restated Certificate").


     2.   REGISTRATION RIGHTS.
          -------------------

          2.1  Certain Definitions.  As used in this Agreement, the following
definitions shall apply:


               "Conversion Stock" means all the shares of Common Stock of the
Company issued or issuable upon the conversion of the Shares (as defined below).

               "Commission" means the Securities and Exchange Commission (the
"SEC") or any other federal agency at the time administering the Securities Act
(as defined below).

               "Form S-3" means such form under the Securities Act as in effect
on the date hereof or any successor registration form under the Securities Act
subsequently adopted by the SEC which permits inclusion or incorporation of
substantial information by reference to other documents filed by the Company
with the Commission.

               "Holder" means any holder of outstanding Registrable Securities;
provided, however, that for all purposes under this Section, the holder of any
Shares, or securities exercisable for Registrable Securities, shall be deemed to
be the Holder of the Registrable Securities into which such Shares are then
convertible.

               "Initiating Holders" means any Holders of not less than 50% of
the Registrable Securities.

          "Register," "registered" and "registration" refer to a registration
effected by preparing and filing a registration statement in compliance with the
Securities Act (and any post-

                                      -4-
<PAGE>

effective amendments filed or required to be filed), and the declaration or
ordering of the effectiveness of such registration statement.

          "Registrable Securities" means (i) the Conversion Stock, (ii) the VLLI
Common Shares, (iii) the COLT Common Shares, (iv) the FMR Common Shares, (v) the
F&W Common Shares, (vi) the Common Stock issuable under the Subscription
Agreement and (vii) any shares of Common Stock of the Company issued or
issuable, directly or indirectly, in respect of such stock described in either
(i), (ii), (iii), (iv) or (iv) upon any stock split, stock dividend,
recapitalization, or similar event, or any shares of Common Stock otherwise
issued or issuable with respect to such stock; provided, however, that
Registrable Securities shall not include any shares of Common Stock which have
previously been registered or sold to the public.

          "Registration Expenses" means all expenses incurred by the Company in
complying with Sections 2.2, 2.3 and 2.4, including, without limitation, all
registration, qualification and filing fees, printing expenses, escrow fees,
fees and disbursements of counsel for the Company, blue sky fees and expenses,
and the expense of any special audits incident to or required by any such
registration (but excluding the compensation of regular employees of the Company
which shall be paid in any event by the Company).  Registration Expenses shall
not include selling commissions, discounts or other compensation paid to
underwriters or other agents or brokers to effect the sale.

          "Securities" means the outstanding Shares and/or the outstanding
Conversion Stock collectively, to the extent each is outstanding from time to
time.

          "Securities Act" means the Securities Act of 1933, as amended, or any
similar federal statute and the rules and regulations of the Commission
thereunder, as shall be in effect at the time.

          "Shares" means the outstanding shares of Series B Stock, Series C
Stock, Series D Stock, Series E Stock, Series F Stock, Series G Stock and Series
H Stock issued under the Series B and C Agreement, Additional Series C
Agreement, Series D Agreement, Series E Agreement, Series F Agreement, Series G
Agreement or Series H Agreement as such agreement may hereafter be amended from
time to time, as applicable.

          2.2  Requested Registration.
               ----------------------

               (a)  Request for Registration. In case the Company shall receive
from Initiating Holders a written request at any time after the earlier of (i)
January 5, 2005 or (ii) a date which is six (6) months after the expiration of
the underwriters' lock-up in connection with the Company's initial public
offering, that the Company effect any registration (which must be an
underwritten registration if such registration is in connection with the
Company's initial public offering), qualification, or compliance with respect to
Registrable Securities held by such Initiating Holders, then the Company shall:

                    (i)  promptly give written notice of the proposed
registration, qualification, or compliance to all other Holders; and

                                      -5-
<PAGE>

                    (ii) as soon as practicable, use its most diligent efforts
to effect all such registration, qualification, or compliance (including,
without limitation, the execution of an undertaking to file post-effective
amendments, appropriate qualification under applicable blue sky or other state
securities laws, and appropriate compliance with applicable regulations issued
under the Securities Act and any other governmental requirements or regulations)
as may be so requested and as would permit or facilitate the sale and
distribution of all or such portion of such Registrable Securities as are
specified in such request, together with all or such portion of the Registrable
Securities of any Holders joining in such request as are specified in a written
request received by the Company within 15 days after the date the Company mails
such written notice;

     Provided, however, that the Company shall not be obligated to take any
action to effect any such registration, qualification, or compliance pursuant to
this Section 2.2:

                         (A)  In any jurisdiction in which the Company would be
required to execute a general consent to service of process in effecting such
registration, qualification, or compliance unless the Company is already subject
to service in such jurisdiction and except as may be required by the Securities
Act;

                         (B)  During the period starting with the date sixty
days prior to the Company's estimated date of filing of, and ending on the date
six months immediately following the effective date of any Securities Act
registration statement pertaining to securities of the Company (other than a
registration of securities in a Rule 145 transaction or with respect to an
employee benefit plan or initiated by security holders);

                         (C)  Unless the aggregate gross offering price thereof
would be at least $5,000,000 or such registration would be for at least 33% of
the Registrable Securities; or

                         (D)  After the Company has effected two such
registrations pursuant to this Section 2.2 and such registrations have been
declared or ordered effective.

          Subject to the foregoing clauses (A) through (D), the Company shall
file a registration statement covering the Registrable Securities so requested
to be registered as soon as practicable, and in any event within 120 days, after
receipt of the request or requests of the Initiating Holders; provided, however,
that if the Company shall furnish to such Holders a certificate signed by the
president of the Company stating that in the good faith judgment of the Board,
it would be seriously detrimental to the Company or its stockholders for such
registration statement to be filed on or before the date filing would be
required and it is therefore essential to defer the filing of such registration
statement, the Company shall have the right to defer such filing for a
reasonable period not to exceed an additional 120 days.

               (b)  Underwriting.  If the Initiating Holders intend to
distribute Registrable Securities by means of an underwriting, the right of any
Holder to registration pursuant to this Section 2.2 shall be conditioned upon
such Holder's participation in such underwriting and the inclusion of such
Holder's Registrable Securities in the underwriting to the extent requested
(unless otherwise

                                      -6-
<PAGE>

mutually agreed by a majority in interest of the Initiating Holders and such
Holder) to the extent provided herein.

          In such event, the Company shall (together with all Holders and
holders of other securities proposing to distribute their securities through
such underwriting) enter into an underwriting agreement in customary form with
the managing underwriter selected for such underwriting by a majority in
interest of the Initiating Holders.  Notwithstanding any other provision of this
Section 2.2, if the managing underwriter advises the Initiating Holders in
writing that marketing factors require a limitation of the number of shares to
be underwritten, then the Company shall so advise all Holders and the other
holders distributing their securities through such underwriting, and the number
of shares of Registrable Securities and other securities that may be included in
the registration and underwriting shall be allocated among all Holders in
proportion, as nearly as practicable, to the respective amounts of securities
entitled to inclusion (determined without regard to any requirement of a request
to be included in such registration) in such registration held by all such
Holders at the time of filing the registration statement, provided, however,
that the number of shares of Registrable Securities to be included in such
underwriting shall not be reduced unless all other securities proposed to be
sold by persons other than the Holders are first entirely excluded from the
underwriting.  No Registrable Securities or other securities excluded from the
underwriting by reason of the underwriter's marketing limitation shall be
included in such registration.  To facilitate the allocation of shares in
accordance with the above provisions, the Company or the underwriters may round
the number of shares allocated to any Holder to the nearest 100 shares.

          If any Holder of Registrable Securities disapproves of the terms of
the underwriting, such person may elect to withdraw therefrom by written notice
to the Company, the managing underwriter and the Initiating Holders.  The
Registrable Securities and/or other securities so withdrawn shall also be
withdrawn from registration, and such Registrable Securities shall not be
transferred in a public distribution prior to 90 days after the effective date
of such registration, or such other shorter period of time as the underwriters
may require.  If by the withdrawal of such Registrable Securities a greater
number of Registrable Securities held by other Holders may be included in such
registration (up to the maximum of any limitation imposed by the underwriters),
then the Company shall offer to all Holders who have included Registrable
Securities in the registration the right to include additional Registrable
Securities in the same proportion and manner used in determining the underwriter
limitation in this Section 2.2(b).

          If the managing underwriter has not limited the number of Registrable
Securities to be underwritten, the Company may include securities for its own
account or for the account of others in such registration if the underwriter so
agrees and if the number of Registrable Securities which would otherwise have
been included in such registration and underwriting will not thereby be limited.

          2.3  Company Registration.
               --------------------

               (a)  Notice of Registration.  If at any time or from time to
time, the Company shall determine to register in an underwritten offering any of
its securities, either for its own account or the account of a security holder
or holders exercising their respective demand registration rights, other than
(i) a registration relating solely to employee benefit plans, (ii) an initial
registration of the

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<PAGE>

Company's shares, or (iii) a registration relating solely to a Commission Rule
145 transaction, the Company shall:

                    (x)  promptly give to each Holder written notice thereof;
and

                    (y)  include in such registration (and any related
qualification under blue sky laws or other compliance), and in any underwriting
involved therein, all the Registrable Securities specified in a written request
by each holder received by the Company within 15 days after the Company mails
such written notice, subject to the provisions below.

               (b)  Underwriting.  The right of any Holder to registration
pursuant to Section 2.3 shall be conditioned upon the participation by such
Holder in such underwriting and the inclusion of the Registrable Securities of
such Holder in the underwriting to the extent provided herein. All Holders
proposing to distribute their securities through such underwriting shall
(together with the Company and the other holders distributing their securities
through such underwriting) enter into an underwriting agreement in customary
form with the managing underwriter selected for such underwriting by the
Company. Notwithstanding any other provision of this Section 2.3, if the
managing underwriter determines that marketing factors require a limitation of
the number of shares to be underwritten, the managing underwriter may limit the
Registrable Securities held by Holders to be included in such registration. The
Company shall so advise all Holders and the other holders distributing their
securities through such underwriting, and the number of shares of Registrable
Securities and other securities that may be included in the registration and
underwriting shall be allocated among all Holders thereof in proportion, as
nearly as practicable, to the respective amounts of securities entitled to
inclusion (determined without regard to any requirement of a request to be
included in such registration) in such registration held by all such Holders at
the time of filing the registration statement, provided that no such inclusion
of Registrable Securities and other securities by the underwriter may reduce the
securities being offered by the Company for its own account. To facilitate the
allocation of shares in accordance with the above provisions, the Company may
round the number of shares allocated to any Holder or holder to the nearest 100
shares. If any Holder or other holder disapproves of the terms of any such
underwriting, he may elect to withdraw therefrom by written notice to the
Company and the managing underwriter. Any securities excluded or withdrawn from
such underwriting shall be withdrawn from such registration, and shall not be
transferred in a public distribution prior to 180 days after the effective date
of the registration statement relating thereto, or such other shorter period of
time as the underwriters may require.

               (c)  Right to Terminate Registration.  The Company shall have the
right to terminate or withdraw any registration initiated by it under this
Section 2.3 prior to the effectiveness of such registration whether or not any
Holder has elected to include securities in such registration.

          2.4  Form S-3 Registration.  In case the Company shall receive from a
Holder or Holders a written request that the Company effect a registration on
Form S-3 and any related qualification or compliance with respect to an amount
of the Registrable Securities owned by such Holder or Holders for which the
anticipated aggregate offering price would be at least $1,000,000, the Company
shall:

                                      -8-
<PAGE>

               (a)  promptly give written notice of the proposed registration,
and any related qualification or compliance to all other Holders; and

               (b)  as soon as practicable, effect such registration and all
such qualifications and compliances as may be so requested and as would permit
or facilitate the sale and distribution of all or such portion of such Holder's
or Holders' Registrable Securities as are specified in such request, together
with all or such portion of the Registrable Securities of any other Holder or
Holders joining in such request as are specified in a written request given
within 15 days after receipt of such written notice from the Company; provided,
however, that the Company shall not be obligated to effect any such
registration, qualification, or compliance pursuant to this Section 2.4: (1) if
Form S-3 is not available for such offering by the Holders; (2) if the Company
shall furnish to the Holders a certificate signed by the president of the
Company stating that in the good faith judgment of the Board, it would be
seriously detrimental to the Company and its stockholders for such Form S-3
Registration to be effected at such time, in which event the Company shall have
the right to defer the filing of the Form S-3 registration statement for a
period of not more than 120 days after receipt of the initiating request of the
Holder or Holders under this Section 2.4; provided, however, that the Company
shall not utilize this right more than once in any twelve month period; (3) if
the Company has, within the six (6) month period preceding the date of such
request, already effected a registration on Form S-3 for the Holders pursuant to
this Section 2.4; or (4) in any jurisdiction in which the Company would be
required to execute a general consent to service of process in effecting such
registration, qualification or compliance unless the Company is already subject
to service in such jurisdiction and except as may be required by the Securities
Act.

          Subject to the foregoing, the Company shall effect such registration,
qualification, or compliance (including, without limitation, the execution of an
undertaking to file post-effective amendments, appropriate qualification under
applicable blue sky or other state securities laws and appropriate compliance
with applicable regulations issued under the Securities Act and any other
governmental requirements or regulations) covering the Registrable Securities
and other securities so requested to be registered as soon as practicable after
receipt of the request or requests of the Holders.  Registrations effected
pursuant to this Section 2.4 shall not be counted as demands for registration or
registrations effected pursuant to Sections 2.2 or 2.3.

          If the registration to be effected pursuant to this Section 2.4 is to
be an underwritten public offering, it shall be managed by an underwriter or
underwriters acceptable to Company selected by a majority in interest of the
Holders requesting registration. In such event, the right of any Holder to
registration pursuant to Section 2.4 shall be conditioned upon the participation
by such Holder in such underwriting and the inclusion of the Registrable
Securities of such Holder in the underwriting to the extent provided herein. If
the managing underwriter so selected determines that marketing factors require a
limitation of the number of shares to be underwritten, the managing underwriter
may limit the Registrable Securities held by such Holders to be included in such
registration. The Company shall so advise such Holders, and the number of shares
of Registrable Securities that may be included in the registration shall be
allocated among such Holders in proportion to the respective amounts of
Registrable Securities which would be held by each of such Holders at the time
of filing of the registration statement. Any Registrable Securities that are so
excluded from the underwriting shall be excluded from the registration.

                                      -9-
<PAGE>

          2.5  Expenses of Registration.  All Registration Expenses incurred in
connection with the registration, qualification or compliance pursuant to
Sections 2.2, 2.3 and 2.4 shall be borne by the Company; provided, however, that
the Company shall not be required to pay for expenses of any registration
proceeding begun pursuant to Section 2.2, the request of which has been
subsequently withdrawn by the Initiating Holders, in which case such expenses
shall be borne by the Holders of securities (including Registrable Securities)
pro rata in accordance with the number of shares initially sought to be
registered requesting or causing such withdrawal, unless at the time of such
withdrawal the Holders have learned of a material adverse change in the
conditions, business, or properties of the Company that could not reasonably
have been known to the Holders at the time of their request.

          2.6  Letter or Opinion of Counsel in Lieu of Registration.  If in the
opinion of counsel for the Company concurred in by counsel for the Holders, no
registration under the Act is required in connection with the disposition of the
Registrable Securities covered by any request made under Sections 2.2, 2.3, and
2.4 in the manner in which they propose to dispose of the Registrable Securities
included in such request, the Company need not comply with such request or
requests; provided, however, that the Company shall not be so relieved of its
obligations under Sections 2.2, 2.3, and 2.4 unless such opinion of counsel for
the Company shall have been mailed by the Company to such Holders within fifteen
(15) days after the Company's receipt of their request or requests; and
provided, further, that if counsel for the Company has opined that no
registration is required in connection with any such disposition, such counsel
shall further opine as to whether the removal of any legend from certificates
representing all shares to which such opinion refers is permissible, and, if so,
the Company shall remove from such certificates all legends no longer required
thereon and shall rescind any stop-transfer instructions previously communicated
to its transfer agent relating to such shares.

          2.7  Lock-up.  Each Investor (or other holder of any Securities)
hereby agrees not to offer, sell, or otherwise dispose of any of the Company's
Common Stock held of record or beneficially owned by such person during a period
of up to 180 days following the effective date of the registration statement for
the Company's initial underwritten public offering as is requested by the
managing underwriter for such offering, provided that (i) all officers and
directors of the Company and all other persons with registration rights are
bound by similar restrictions, (ii) the restriction set forth in this section
shall only apply to securities purchased privately from the Company, and (iii)
any discretionary waiver or termination of the restriction set forth in this
section (or any similar lock-up provision to which the Company is a party) by
the Company or the underwriter shall apply to all the Investors on a pro rata
basis (according to the total number of Securities owned by each Investor).
Such restriction shall not apply to shares registered in such offering.  In
order to enforce this provision, the Company may impose stop-transfer
instructions with respect to such shares until the end of such period.

          2.8  Registration Procedures.  If and whenever the Company is required
by the provisions of this Section to use its most diligent efforts to effect
promptly the registration of Registrable Securities, the Company shall:

               (a)  Prepare and file with the Commission a registration
statement with respect to such Registrable Securities and use its most diligent
efforts to cause such registration statement to become and remain effective as
provided herein.

                                      -10-
<PAGE>

               (b)  Prepare and file with the Commission such amendments and
supplements to such registration statement and the prospectus used in connection
therewith as may be necessary to keep such registration statement effective and
current and to comply with the provisions of the Securities Act with respect to
the sale or other disposition of all Registrable Securities covered by such
registration statement, including such amendments and supplements as may be
necessary to reflect the intended method of disposition of the prospective
seller or sellers of such Registrable Securities, but for no longer than one
hundred twenty (120) days subsequent to the effective date of such registration
in the case of a registration statement on Form S-1 (or any similar form of
registration statement required to set forth substantially identical
information) and for no longer than ninety (90) days in the case of a
registration statement on Form S-3.

               (c)  Furnish to each prospective seller of Registrable Securities
such number of copies of a prospectus, including a preliminary prospectus, in
conformity with the requirements of the Securities Act, and such other
documents, as such seller may reasonably request in order to facilitate the
public sale or other disposition of the Registrable Securities of such seller.

          2.9  Indemnification.  In the event any of the Registrable Securities
are included in a registration statement under this Section:

               (a)  The Company will indemnify each Holder, each of its officers
and directors and partners and such Holder's separate legal counsel and
independent accountants, and each person controlling such Holder within the
meaning of Section 15 of the Securities Act, and each underwriter, if any, and
each person who controls any underwriter within the meaning of Section 15 of the
Securities Act, against all expenses, claims, losses, damages or liabilities (or
actions in respect thereof), including any of the foregoing incurred in
settlement of any litigation, commenced or threatened, arising out of or based
on any untrue statement (or alleged untrue statement) of a material fact
contained in any registration statement, prospectus, offering circular or other
document, or any amendment or supplement thereto, incident to any such
registration, qualification or compliance, or based on any omission (or alleged
omission) to state therein a material fact required to be stated therein or
necessary to make the statements therein, in light of the circumstances in which
they were made, not misleading, or any violation by the Company of any rule or
regulation promulgated under the Securities Act applicable to the Company in
connection with any such registration, qualification or compliance, and the
Company will reimburse each such Holder, each of its officers and directors and
partners and such Holders' separate legal counsel and independent accountants
and each person controlling such Holder, each such underwriter and each person
who controls any such underwriter, for any legal and any other expenses
reasonably incurred in connection with investigating, preparing or defending any
such claim, loss, damage, liability or action, provided that the Company will
not be liable in any such case to the extent that any such claim, loss, damage,
liability or expense arises out of or is based on any untrue statement or
omission or alleged untrue statement or omission, made in reliance upon and in
conformity with written information furnished to the Company by an instrument
duly executed by such Holder or underwriter and stated to be specifically for
use therein.

               (b)  Each Holder will, if Registrable Securities held by such
Holder are included in the securities as to which such registration,
qualification or compliance is being effected,

                                      -11-
<PAGE>

severally and not jointly indemnify the Company, each of its directors and
officers and its legal counsel and independent accountants, each underwriter, if
any, of the Company's securities covered by such a registration statement, each
person who controls the Company or such underwriter within the meaning of
Section 15 of the Securities Act, and each other such Holder, each of its
officers and directors and each person controlling such Holder within the
meaning of Section 15 of the Securities Act, against all claims, losses, damages
and liabilities (or actions in respect thereof) arising out of or based on any
untrue statement (or alleged untrue statement) of a material fact contained in
any such registration statement, prospectus, offering circular or other
document, or any omission (or alleged omission) to state therein a material fact
required to be stated therein or necessary to make the statements therein not
misleading, and will reimburse the Company, such Holders, such directors,
officers, persons, underwriters or control persons for any legal or any other
expenses reasonably incurred in connection with investigating or defending any
such claim, loss, damage, liability or action, in each case to the extent, but
only to the extent, that such untrue statement (or alleged untrue statement) or
omission (or alleged omission) is made in such registration statement,
prospectus, offering circular or other document in reliance upon and in
conformity with written information furnished to the Company by an instrument
duly executed by such Holder and stated to be specifically for use therein;
provided, however, that the obligations of such Holders hereunder shall be
limited to an amount equal to the net proceeds to each such Holder of
Registrable Securities sold as contemplated herein.

               (c)  Each party entitled to indemnification under this Section
(the "Indemnified Party") shall give notice to the party required to provide
indemnification (the "Indemnifying Party") promptly after such Indemnified Party
has actual knowledge of any claim as to which indemnity may be sought, and shall
permit the Indemnifying Party to assume the defense of any such claim or any
litigation resulting therefrom, provided that counsel for the Indemnifying
Party, who shall conduct the defense of such claim or litigation, shall be
approved by the Indemnified Party (whose approval shall not unreasonably be
withheld), and the Indemnified Party may participate in such defense at such
party's expense. No Indemnifying Party, in the defense of any such claim or
litigation, shall, except with the consent of each Indemnified Party, consent to
entry of any judgment or enter into any settlement which does not include as an
unconditional term thereof the giving by the claimant or plaintiff to such
Indemnified Party of a release from all liability in respect to such claim or
litigation.

               (d)  If the indemnification provided for in this Section 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 the Indemnified
Party, shall contribute to the amount paid or payable by such Indemnified Party
with respect to such loss, liability, claim, damage or expense in the proportion
that is appropriate to reflect the relative fault of the Indemnifying Party and
the Indemnified Party 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 the Indemnified Party shall be determined by reference to, among other
things, whether the untrue or alleged untrue statement of 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' relative
intent, knowledge, access to information and opportunity to correct or prevent
such statement or omission provided, however, that the obligations of such
Indemnifying Party hereunder shall be limited to an

                                      -12-
<PAGE>

amount equal to the net proceeds to each such Holder of Registrable Securities
sold as contemplated herein.

          2.10 Information by Holder.  The Holder or Holders of Registrable
Securities included in any registration shall furnish to the Company such
information regarding such Holder or Holders and the distribution proposed by
such Holder or Holders as the Company may request in writing and as shall be
required in connection with any registration, qualification or compliance
referred to in this Section.

          2.11 Rule 144 Reporting. With a view to making available the benefits
of certain rules and regulations of the Commission which may at any time permit
the sale of the Securities to the public without registration, after such time
as a public market exists for the Common Stock of the Company and until five
years from the date hereof, the Company shall use its best efforts to:

               (a)  Make and keep public information available, as those terms
are understood and defined in Rule 144 under the Securities Act, beginning 90
days after (i) the effective date of the first registration statement filed by
the Company for an offering of its securities to the general public, (ii) the
Company registers a class of securities under Section 12 of the Securities
Exchange Act of 1934, as amended, or (iii) the Company issues an offering
circular meeting the requirements of Regulation A under the Securities Act;

               (b)  File with the Commission in a timely manner all reports and
other documents required of the Company under the Securities Act and the
Securities Exchange Act of 1934, as amended (at any time after it has become
subject to such reporting requirements);

               (c)  Furnish to any Holder promptly upon request a written
statement as to its compliance with the reporting requirements of Rule 144 (at
any time after 90 days after the effective date of the first registration
statement filed by the Company for an offering of its securities to the general
public), and of the Securities Act and the Securities Exchange Act of 1934 (at
any time after it has become subject to such reporting requirements), a copy of
the most recent annual or quarterly report of the Company, and such other
reports and documents of the Company and other information in the possession of
or reasonably obtainable by the Company as a Holder may reasonably request in
availing itself of any rule or regulation of the Commission allowing a Holder to
sell any such securities without registration.

     3.   RIGHT OF FIRST OFFER.
          --------------------

          3.1  The Company hereby grants to each of the Investors identified on
Exhibit A as "Selected Investors," the right of first offer to purchase pro
rata, all (or any part) of New Securities (as defined herein) that the Company
may from time to time propose to sell and issue.  Each Selected Investor's pro
rata share, for purposes of this right of first offer, is the ratio, the
numerator of which is the number of shares of Common Stock issued or issuable to
such Selected Investor pursuant to the conversion of all shares of Preferred
Stock of the Company which it holds (appropriately adjusted for any
combinations, consolidations, stock splits, stock distributions, or stock
dividends with respect to such Shares), and the denominator of which is the
total number of outstanding shares of Common

                                      -13-
<PAGE>

Stock assuming conversion of all outstanding shares of Preferred Stock. This
right of first offer shall be subject to the following provisions:

          3.2  "New Securities" shall mean any Common Stock or shares of
Preferred Stock of the Company, whether now authorized or not, and any rights,
options or warrants to purchase said Common Stock or Preferred Stock, and
securities of any type whatsoever that are, or may become convertible into said
Common Stock or Preferred Stock; provided, however, that "New Securities" does
not include (i) securities issuable upon conversion of or with respect to any
series of Preferred Stock; (ii) securities offered to the public pursuant to a
registration statement filed under the Securities Act; (iii) securities issued
pursuant to the acquisition of another corporation by the Company by merger or
purchase of all or substantially all of the assets thereof; (iv) securities
offered or issued to a customer, strategic corporate partner or potential
strategic corporate partner and approved by the Board; (v) shares of the
Company's Common Stock (or related options) issued to employees, officers,
directors, or consultants of the Company pursuant to incentive stock option or
stock purchase plans and approved by the Board; or (vi) shares of the Company's
Preferred Stock or Common Stock issued in connection with any stock split, stock
dividend or recapitalization by the Company.

          3.3  In the event that the Company proposes to undertake an issuance
of New Securities, it shall deliver to each Selected Investor written notice of
its intention, describing the type of New Securities, the price, and the general
terms upon which the Company proposes to issue the same. Each Selected Investor
shall have fifteen (15) days from the date of delivery of any such notice to
agree to purchase its pro rata share as provided above of such New Securities
for the price and upon the general terms specified in the notice by giving
written notice to the Company and stating therein the quantity of New Securities
to be purchased. Each Selected Investor shall have a right of over-allotment
such that if any Selected Investor fails to exercise its right hereunder to
purchase its pro rata portion of New Securities, as provided above, the Company
shall so notify the other Selected Investors and the other Selected Investors
may purchase the non-purchasing Selected Investor's portion on a pro rata basis,
within fifteen (15) days from the date of delivery of such notice as follows:
unless the exercising Selected Investors agree otherwise in writing, each
exercising Selected Investor will have the right to purchase that number of New
Securities that is obtained by multiplying the total number of New Securities by
a fraction (x) the numerator of which is the sum of the number of shares of
stock on an as-if converted to Common Stock basis then owned by such Selected
Investor and (y) the denominator of which is the sum of the total number of
shares of stock on an as-if converted to Common Stock basis then held by all
Selected Investors then exercising their right of first offer hereunder. Any
remaining New Securities may be purchased by Selected Investors according to the
same principle of proration until all such New Securities are allocated to
Selected Investors exercising their right of first offer hereunder. A Selected
Investor which elects to purchase its pro rata share of New Securities shall pay
the price therefor within thirty (30) days of the date on which it delivers its
election to purchase.

          3.4  To the extent the Selected Investors do not exercise the right of
first offer within said fifteen (15) day period, the Company shall have one
hundred twenty (120) days thereafter to sell the New Securities respecting which
the Selected Investors' rights were not exercised, at a price and upon general
terms no more favorable to the purchasers thereof than specified in the
Company's notice. In the event the Company has not sold the New Securities
within such one hundred twenty

                                      -14-
<PAGE>

(120) day period, the Company shall not thereafter issue or sell any New
Securities without first offering such securities to the Selected Investors in
the manner provided above.

          3.5  The right of first offer granted under this Section 3 shall
expire immediately prior to the closing of the sale of the Company's Common
Stock in an underwritten public offering registered under the Securities Act.

     4.   ASSIGNMENT AND AMENDMENT.
          ------------------------

          4.1  Assignment.  Notwithstanding anything herein to the contrary:

               (a)  Information Rights.  The rights of an Investor under
Sections 1.1 or 1.2 hereof may be assigned only to a party who acquires from an
Investor (or an Investor's permitted assigns) at least 15% of the shares of
Series B Stock, Series C Stock, Series D Stock, Series E Stock, Series F Stock,
Series G Stock and/or Series H Stock originally purchased under the Series B and
C Agreement, Additional Series C Agreement, Series D Agreement, Series E
Agreement, Series F Agreement, Series G Agreement or Series H Agreement as
applicable, and/or an equivalent number (on an as-converted basis) of shares of
Conversion Stock. The aforementioned limitation on the assignment of information
rights shall not apply to the transfer of shares that occurs in a distribution
from an Investor which is a corporation to an affiliate (as defined in Rule 144
promulgated under the Securities Act) thereof, provided that all such transferee
affiliates and such transferor shall be treated as one entity under Section 1.

               (b)  Registration Rights.  The rights to cause the Company to
register securities granted under Section 2 may be assigned to a transferee or
assignee in connection with the transfer or assignment of shares of Registrable
Securities only if the transfer or assignor provides prior written notice
thereof to the Company and (i) such transferee or assignee holds at least 2% of
the outstanding shares of the Company's capital stock (assuming conversion of
all Preferred Stock to Common Stock) on the date of such assignment (ii) the
transfer of such shares occurs in a distribution from an Investor which is a
partnership to a partner thereof, or (iii) the transfer of such shares occurs in
a distribution from an Investor which is a corporation to an affiliate (as
defined in Rule 144 promulgated under the Securities Act) thereof, provided that
all such transferee affiliates and such transferor shall be treated as one
entity under Section 2.

               (c)  Right of First Offer.  The right of first offer provided in
Section 3 may be assigned to any affiliate or other transferee of a Selected
Investor provided that such other transferee holds at least 2% of the
outstanding shares of the Company's capital stock (assuming conversion of all
Preferred Stock to Common Stock) on the date of such assignment.  The
aforementioned limitation on the assignment of the right of first offer shall
not apply to the transfer of shares that occurs in a distribution from an
Investor which is a corporation to an affiliate (as defined in Rule 144
promulgated under the Securities Act) thereof, provided that all such transferee
affiliates and such transferor shall be treated as one entity under Section 3.

          4.2  Additional Registration Rights.  From the date of this Agreement,
the Company shall not, without the prior written consent of the Company and
Investors (and/or any of their permitted successors or assigns) holding shares
of Series B Stock, Series C Stock, Series D Stock, Series E

                                      -15-
<PAGE>

Agreement, Series F Stock, Series G Stock, Series H Stock and/or Conversion
Stock representing and/or convertible into a majority of all the Registrable
Securities, enter into any agreement with any holder or prospective holder of
any securities of the Company which would allow such holder or prospective
holder (a) to include such securities in any registration filed under Section
2.2 hereof, unless under the terms of such agreement, such holder or prospective
holder may include such securities in any such registration only to the extent
that the inclusion of his securities will not reduce the amount of the
Registrable Securities of the Holders which is included or (b) to make a demand
registration which could result in such registration statement being declared
effective prior to the earlier of either of the dates set forth in 2.2(a) or
within 120 days of the effective date of any registration effected pursuant to
Section 2.2.

          4.3  Amendment of Rights.  Any provision of this Agreement may be
amended and the observance thereof may be waived (either generally or in a
particular instance and either retroactively or prospectively), only with the
written consent of the Company and Investors (and/or any of their permitted
successors or assigns) holding shares of Series B Stock, Series C Stock, Series
D Stock, Series E Stock, Series F Stock, Series G Stock, Series H Stock and/or
Conversion Stock representing and/or convertible into a majority of all the
Registrable Securities.  Any amendment or waiver made in accordance with this
Section 4.3 shall be binding upon all of the parties hereto.

          4.4  New Investors.  Notwithstanding anything herein to the contrary,
if pursuant to Section 2.2 of the Series H Agreement, additional parties may
purchase shares of Series H Stock as "New Investors" thereunder, then each such
New Investor shall become a party to this Agreement as an "Investor" hereunder,
without the need of any consent, approval or signature of any Investor when such
New Investor has both: (a) purchased shares of Series H Stock under the Series H
Agreement and paid the Company all consideration payable for such shares and (b)
executed one or more counterpart signature pages to this Agreement as an
"Investor", with the Company's consent.

     5.   GENERAL PROVISIONS.
          ------------------

          5.1  Notices.  All notices and other communications required or
permitted hereunder shall be in writing and shall be mailed by registered or
certified mail, postage prepaid, or otherwise delivered by hand or by messenger,
addressed (i) if to an Investor, at such Investor's respective address as set
forth in Exhibit A hereto, or at such other address as such Investor shall have
furnished to the Company in writing, (ii) if to any other holder of any
Securities, at such address as such holder shall have furnished the Company in
writing, or, until any such holder so furnishes an address to the Company, then
to and at the address of the last holder of such Securities who has so furnished
an address to the Company, or (iii) if to the Company, one copy to its address
set forth on the first page of this agreement and addressed to the attention of
the Corporate Secretary, or at such other address as the Company shall have
furnished to the Investors, and another copy to the Company's legal counsel to
the attention of Richard L. Dickson, Esq. of Fenwick & West LLP, Two Palo Alto
Square, Palo Alto, California 94306.

          5.2  Entire Agreement.  This Agreement constitutes the full and entire
understanding and agreement between the parties with regard to the subject
matters hereof.

                                      -16-
<PAGE>

          5.3  Governing Law.  This Agreement shall be governed by and construed
exclusively in accordance with the internal laws of the State of California as
applied to agreements among California residents entered into and to be
performed entirely within California, excluding that body of law relating to
conflict of laws and choice of law.

          5.4  Severability.  If any provision of this agreement is held to be
unenforceable under applicable law, then such provision shall be excluded from
this agreement and the balance of this agreement shall be interpreted as if such
provision were so excluded and shall be enforceable in accordance with its
terms. The court in its discretion may substitute for the excluded provision an
enforceable provision which in economic substance reasonably approximates the
excluded provision.

          5.5  Third Parties.  Nothing in this Agreement, express or implied, is
intended to confer upon any person, other than the parties hereto and their
successors and assigns, any rights or remedies under or by reason of this
Agreement.

          5.6  Successors and Assigns.  Except as otherwise expressly limited
herein, the provisions hereof shall inure to the benefit of, and be binding
upon, the successors, assigns, heirs, executors, and administrators of the
parties hereto.

          5.7  Headings.  The headings and captions used in this Agreement are
used for convenience only and are not to be considered in construing or
interpreting this Agreement.  All references in this Agreement to sections,
paragraphs, exhibits and schedules shall, unless otherwise provided, refer to
sections and paragraphs hereof and exhibits and schedules attached hereto, all
of which exhibits and schedules are incorporated herein by this reference.

          5.8  Adjustments for Stock Splits, Etc.  Wherever in this Agreement
there is a reference to a specific number of shares of Common Stock or Preferred
Stock of the Company of any class or series, then, upon the occurrence of any
subdivision, combination or stock dividend of such class or series of stock, the
specific number of shares so referenced in this Agreement shall automatically be
proportionally adjusted to reflect the affect on the outstanding shares of such
class or series of stock by such subdivision, combination or stock dividend.

          5.9  Aggregation of Stock.  All shares held or acquired by affiliated
entities or persons shall be aggregated together for the purpose of determining
the availability of any rights under this Agreement.

          5.10  Prior Rights Agreements Superseded.  Pursuant to Section 4.3 of
the Prior Rights Agreement, the undersigned parties who are parties to such
Prior Rights Agreement hereby amend and restate the Prior Rights Agreement to
read in its entirety as set forth in this Agreement, all with the intent and
effect that the Prior Rights Agreement shall be hereby terminated and entirely
replaced and superseded by this Agreement.  Internet Initiative Japan, COLT, FMR
and F&W hereby agree that any prior registration rights with respect to
securities of the Company held by them shall hereby be superseded by this
Agreement.

          5.11  Delays or Omissions.  No delay or omission to exercise any
right, power, or remedy accruing to any party upon any breach or default under
this agreement, shall be deemed a waiver of any other breach or default
theretofore or thereafter occurring. Any waiver, permit, consent,

                                      -17-
<PAGE>

or approval of any kind or character on the part of any party of any breach or
default under this agreement, or any waiver on the part of any party of any
provisions or conditions of this agreement, must be in writing and shall be
effective only to the extent specifically set forth in such writing. All
remedies, either under this agreement or by law or otherwise afforded to any of
the parties, shall be cumulative and not alternative.

          5.12  Counterparts.  This agreement may be executed in any number of
counterparts, each of which shall be deemed an original and enforceable against
the parties actually executing such counterpart, and all of which together shall
constitute one instrument.


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                                      -18-
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the date and year first above written.

COMPANY:
-------

ONI Systems Corp.

By:
   ----------------------------------

Name:
     --------------------------------

Title:
      -------------------------------

INVESTORS:
---------