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                                                                  Exhibit 4.1

                        COGENT COMMUNICATIONS GROUP, INC.

                              AMENDED AND RESTATED
                             STOCKHOLDERS AGREEMENT

         STOCKHOLDERS AGREEMENT made this 16th day of October, 2001 by and
among (i) Cogent Communications Group, Inc., a Delaware corporation (the
"Company"), (ii) David Schaeffer (the "Founder"), and each other Person
(other than a Purchaser, as defined below) who, after the date hereof,
acquires at least one percent (1%) of the number of shares of Common Stock or
other equity securities of the Company outstanding and joins in and becomes a
party to this Agreement by executing and delivering to the Company an
Instrument of Accession in the form of Schedule II hereto (the Founder and
such other persons being referred to collectively as the "Holders" and
singularly as a "Holder"), and (iii) those persons whose names are set forth
under the heading "Purchasers" on Schedule I hereto (the "Purchasers").

                                   WITNESSETH:

         WHEREAS, simultaneously herewith, the Company and certain of the
Purchasers (the "Series C Purchasers") have consummated the transactions
contemplated by that certain Series C Participating Convertible Preferred Stock
Purchase Agreement by and among the Company and the Series C Purchasers, dated
as of the date hereof (the "Purchase Agreement"), pursuant to which the Series C
Purchasers have agreed, subject to the terms and conditions set forth therein,
to purchase up to 52,137,643 shares of the Company's Series C Participating
Convertible Preferred Stock, par value $.001 per share (the "Series C Preferred
Stock");

         WHEREAS, the Founder and certain of the Purchasers who purchased the
Series A Participating Convertible Preferred Stock, par value $.001 per share,
of the Company (the "Series A Preferred Stock"), and Series B Participating
Convertible Preferred Stock, par value $.001 per share, of the Company (the
"Series B Preferred Stock," and together with the "Series A Preferred Stock" and
the "Series C Preferred Stock," the "Preferred Stock"), are parties to that
certain Stockholders Agreement, dated as of March 14, 2001 (the "Original
Stockholders Agreement"), and in connection with the consummation of the
transactions contemplated by the Purchase Agreement, the Company, the Founder
and such Purchasers, constituting signatories sufficient under Section 15 of the
Original Stockholders Agreement to amend the Original Stockholders Agreement,
desire to amend and restate the Original Stockholders Agreement as set forth
herein and execute and deliver this Agreement, setting forth herein certain
terms and conditions governing their relative ownership of the Shares (as
hereinafter defined).

         NOW THEREFORE, in consideration of the mutual covenants herein
contained and other good and valuable consideration, the receipt and sufficiency
of which is hereby acknowledged, the Company, the Holders and the Purchasers
hereby agree as follows:

                  1.       PROHIBITED TRANSFERS.

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                           (a)  TRANSFERS BY HOLDERS.  The Holders shall not
sell, assign, transfer, pledge, hypothecate, mortgage or dispose of, by gift or
otherwise, or in any way encumber, all or any part of the Shares (as hereinafter
defined) owned by them except in compliance with the terms of this Agreement.
For purposes of this Agreement, the term "Shares" shall mean and include all
shares of Common Stock of the Company and all shares of any class or series of
equity securities or equity-backed securities of the Company or any subsidiary,
including without limitation, capital stock (including any shares of treasury
stock) or rights, options, warrants or other securities convertible into or
exercisable or exchangeable for capital stock or any debt security which by its
terms is convertible into or exchangeable for any equity security or has any
other equity feature or any security that is a combination of debt and, in any
event that is owned by the Holders, whether presently held or hereafter
acquired. Notwithstanding the foregoing, after the date on which the Company
becomes obligated to file reports pursuant to the Securities Exchange Act of
1934, as amended (the "Public Company Date"), this Section 1(a) shall apply only
to the Founder and no other Holder.

                           (b)  TRANSFER BY THE FOUNDER WHILE AN EMPLOYEE.
Notwithstanding the provisions of Section 1(a) and except as set forth in
Section 4, for so long as the Founder is employed by the Company or Cogent
Communications, Inc., the Founder shall not sell, assign or otherwise transfer
any shares of Common Stock held by the Founder (the "Founder's Common") for a
period of three (3) years from February 7, 2000; provided, that the foregoing
restriction on sales by the Founder shall terminate on the first to occur of (i)
the closing of a firmly underwritten public offering pursuant to an effective
registration statement under the Securities Act of 1933, as amended, covering
the offer and sale of Common Stock of the Company in which (a) the pre-money
valuation of the Company is at least $500,000,000 and (b) the gross cash
proceeds (before underwriting discounts, commissions and fees) are at least
$50,000,000 (a "Qualified Offering"), (ii) the sale of the Company or control
thereof, whether by merger, sale, recapitalization or similar corporate event or
the transfer of more than a majority of its capital stock (calculated on an as
converted, fully diluted basis) or assets (collectively, a "Transfer of
Control"), or (iii) conversion into Common Stock of all then outstanding shares
of Preferred Stock (each of the event set forth in clauses (i)-(iii) hereof, a
"Corporate Event").

                  (c) TRANSFERS BY THE FOUNDER WHILE NOT AN EMPLOYEE.
Notwithstanding the provisions of Section 1(a), if the Founder is no longer
employed by the Company or Cogent Communications, Inc. for whatever reason, the
foregoing restrictions on transfers of Founder's Common shall be lifted as to
25% of the Founder's Common plus such additional percentage of as is obtained by
dividing the actual number of days elapsed from February 7, 2000 by 1460 (as
adjusted for stock splits, stock dividends, reclassifications, recapitalizations
or other similar events). The restrictions contained in this Section 1(c) shall
be of no further force and effect from and after the first to occur of (i) a
Qualified Offering, (ii) a Transfer of Control or (iii) conversion into Common
Stock of a majority of all then outstanding shares of Preferred Stock

         2. RIGHT OF REFUSAL ON DISPOSITIONS BY THE HOLDERS. Except as set forth
in Section 4, if at any time prior to the consummation of a Qualified Offering
any of the Holders wishes to sell, assign, transfer or otherwise dispose of any
or all Shares owned by such Holder pursuant to the terms of a bona fide offer
received from a third party, the Holder shall submit a written offer

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to sell such Shares to the Purchasers (with a copy to the Company) on terms and
conditions, including price, not less favorable to the Purchasers than those on
which he proposes to sell such Shares to such third party (the "Offer"). The
Offer shall disclose the identity of the proposed purchaser or transferee, the
Shares proposed to be sold or transferred, the agreed terms of the sale or
transfer and any other material facts relating to the sale or transfer. Within
thirty (30) days after receipt of the Offer, each Purchaser and each Qualified
Transferee, if any, shall give notice to the Holder of its intent to purchase
all or any portion of the offered Shares on the same terms and conditions as set
forth in the Offer. Each Purchaser and Qualified Transferee shall have the right
to purchase that number of the Shares as to which the Offer applies as shall be
equal to the aggregate number of such Shares multiplied by a fraction, the
numerator of which is the number of shares of Common Stock of the Company then
owned by such Purchaser or Qualified Transferee (as applicable) (calculated on
an as converted basis, and including any shares of Common Stock deemed to be
beneficially owned by such Purchaser pursuant to Rule 13d-3 promulgated under
the Securities Exchange Act of 1934 ("Rule 13d-3")) and the denominator of which
is the aggregate number of shares of said Common Stock then issued and
outstanding and held by (and deemed to be beneficially owned by) all the
Purchasers (calculated on an as converted basis). The amount of Shares each
Purchaser or Qualified Transferee, as that term is defined below, is entitled to
purchase under this Section 2 shall be referred to as such Purchaser's "Pro Rata
Fraction." Each Purchaser shall have the right to transfer his right to any Pro
Rata Fraction or part thereof to any Qualified Transferee. If any Purchaser or
Qualified Transferee does not wish to purchase or to transfer his right to
purchase his Pro Rata Fraction, then any Purchasers or Qualified Transferees who
so elect shall have the right to purchase, on a pro rata basis with any other
Purchasers or Qualified Transferees who so elect, any Pro Rata Fraction not
purchased by a Purchaser or Qualified Transferee. Each Purchaser or Qualified
Transferee shall act upon the Offer as soon as practicable after receipt from
the Company of notice that it has not elected to purchase all of the offered
Shares, and in all events within fifteen (15) days after receipt thereof. Each
Purchaser and Qualified Transferee shall have the right to accept the Offer as
to all or part of the Remaining Offered Shares offered thereby. If a Purchaser
or Qualified Transferee shall elect to purchase all or part of such Purchaser's
or Qualified Transferee's Pro rata Fraction, said Purchaser or Qualified
Transferee shall individually communicate in writing such election to purchase
to whichever of the Holders has made the Offer, which communication shall be
delivered by hand or delivered to such Holder at the address set forth in
Section 8 below and shall, when taken in conjunction with the Offer be deemed to
constitute a valid, legally binding and enforceable agreement for the sale and
purchase of the Shares covered thereby.

         If the Purchasers, taken together, do not agree to purchase all of the
Shares offered by a Holder pursuant to and within thirty (30) days after receipt
of the Offer, and consummate such purchase within forty-five (45) days after
receipt of the Offer, such Shares subject to the Offer as shall not have been
purchased may be sold by such Holder at any time within 90 days after the
expiration of the Offer, but subject to the provisions of Section 3 below. Any
such sale shall be at not less than the price and upon other terms and
conditions, if any, not more favorable to the purchaser than those specified in
the Offer. Any Shares not sold within such 90-day period shall continue to be
subject to the requirements of a prior offer and re-sale pursuant to this
Section.

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         For purposes hereof, a "Qualified Transferee' shall mean any person (i)
who is a Purchaser, (ii) who is an "affiliated person" of a Purchaser, as that
term is defined in the Investment Company Act of 1940, (iii) who is a partner,
member or stockholder of a Purchaser that is a partnership, limited liability
company or corporation, as applicable, and who is offered a pro rata right,
based on his, her or its interest in the Purchaser, to acquire the Shares
offered by a Holder pursuant to this Section 2, or (iv) who acquires at least
twenty five percent (25%) of the shares of Preferred Stock issued by the Company
to any Purchaser (as adjusted for stock splits, stock dividends,
reclassifications, recapitalizations or other similar events). With respect to
any transfers of Shares by any Holder other than the Founder, the Founder shall
be deemed to be a Purchaser for purposes of this Section 2. In addition,
beginning on the Public Company Date, the term "Holder" in this Section 2 shall
be deemed to mean the Founder.

             3. RIGHT OF PARTICIPATION IN SALES BY THE FOUNDER. Except as set
forth in Section 4, if at any time the Founder wishes to sell, transfer or
otherwise dispose of any Shares owned by him to any person (the "Acquiror") in a
transaction which is subject to the provisions of Section 2 hereof, and such
sale, transfer or other disposition would, when combined with all prior sales,
transfers and other dispositions by the Founder, result in the transfer by the
Founder of Shares representing more than twenty-five percent (25%) of the total
number of shares of Founder's Common with respect to which the restrictions on
transfer set forth herein have elapsed or otherwise do not apply, each Purchaser
shall have the right to require, as a condition to such sale or disposition,
that the Acquiror purchase from said Purchaser at the same price per Share and
on the same terms and conditions as involved in such sale or disposition by the
Founder the same percentage of shares of Common Stock owned (and deemed to be
beneficially owned under Rule 13d-3) by such Purchaser as such sale or
disposition represents with respect to the number of shares of Founder's Common
(calculated on an as converted, fully diluted basis) owned by the Founder
immediately prior to such sale. Each Purchaser wishing so to participate in any
such sale or disposition shall notify the Founder of such intention as soon as
practicable after receipt of the Offer made pursuant to Section 2, and in all
events within fifteen (15) days after receipt thereof. If a Purchaser shall
elect to participate in such sale or disposition, said Purchaser shall
individually communicate such election to the Founder, which communication shall
be delivered by hand or mailed to the Founder at the address set forth in
Section 8 below. The Founder and/or each participating Purchaser shall sell to
the Acquiror all, or at the option of the Acquiror, any part of the Stock (as
defined in Section 5 below) proposed to be sold by them at not less than the
price and upon other terms and conditions, if any, not more favorable to the
Acquiror than those set forth in the Offer; PROVIDED, HOWEVER, that any purchase
of less than all of such Stock by the Acquiror shall be made from the Founder
and/or each participating Purchaser based upon a fraction, the numerator of
which is the number of shares of Stock of the Company then owned by the Founder
or such participating Purchaser (including any shares of Common Stock deemed to
be owned under Rule 13d-3) and the denominator of which is the aggregate number
of shares of Stock held by (and deemed to be held by) the Founder and all of the
participating Purchasers. The Founder shall use his best efforts to obtain the
agreement of the Acquiror to the participation of the participating Purchasers
in the contemplated sale, and shall not sell any Stock to such Acquiror if such
Acquiror declines to permit the participating Purchasers to participate pursuant
to the terms of this Section 3. The provisions of this Section 3

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shall not apply to the sale of any Shares by the Founder (i) to a Purchaser
pursuant to an Offer under Section 2 or (ii) made upon or after the occurrence
of a Corporate Event.

         4. PERMITTED TRANSFERS. Anything herein to the contrary
notwithstanding, the provisions of Sections 1, 2 and 3 shall not apply to: (a)
any transfer of Shares by a Holder by gift or bequest or through inheritance to,
or for the benefit of, any member or members of his immediate family; (b) any
transfer of Shares by a Holder to a trust in respect of which he serves as
trustee, provided that the trust instrument governing said trust shall provide
that such Holder, as trustee, shall retain sole and exclusive control over the
voting and disposition of said Shares until the termination of the applicable
restrictions on transfer under this Agreement; (c) any sale of Common Stock in a
public offering pursuant to a registration statement filed by the Company with
the Securities and Exchange Commission; (d) any repurchase of shares of Common
Stock from officers, employees, directors or consultants of the Company which
are subject to restrictive stock purchase agreements under which the Company has
the option to repurchase such shares upon the occurrence of certain events,
including termination of employment; and (e) any pledge, hypothecation or other
similar financing transaction in which the transferring Holder continues to have
the sole and exclusive authority and right to vote the shares subject to such
pledge, hypothecation or other financing transaction. In the event of any such
transfer, other than pursuant to subsection (c) of this Section 4, the
transferee of the Shares shall hold the Shares so acquired with all the rights
conferred by, and subject to all the restrictions imposed by, this Agreement on
the party from whom the transferee received the Shares, and as a condition to
such transfer, each such transferee shall execute and deliver a written
agreement agreeing to be bound by the provisions of this Agreement.

         5. ELECTION OF DIRECTORS; ISSUANCE OF OPTIONS.

                  (a) ELECTION OF DIRECTORS. Each of the parties hereto agrees
to vote all of the Stock (as hereinafter defined) of the Company now owned or
hereafter acquired by such party (and attend, in person or by proxy, all
meetings of stockholders called for the purpose of electing directors), and the
Company agrees to take all actions (including, but not limited to the nomination
of specified persons) to cause and maintain the election to the Board of
Directors of the Company, to the extent permitted pursuant to the Company's
certificate of incorporation, of the following:

                           (i)      two (2) individuals designated by the
holders of a majority of the shares of Common Stock (other than any shares
received on conversion of the Preferred Stock) (the designees of the holders of
Common Stock under this subsection shall initially be David Schaeffer and H.
Helen Lee);

                           (ii)     two (2) individuals designated by the
holders of a majority in interest of the then outstanding Series A Preferred
Stock (the designees of the holders of Series A Preferred Stock under this
subsection shall initially be Erel Margalit and James Wei);

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                           (iii)    one (1) individual designated by the holders
of a majority in interest of the then outstanding Series B Preferred Stock (the
designee of the holders of Series B Preferred Stock under this subsection shall
initially be Edward Glassmeyer);

                           (iv)     one (1) individual designated by the holders
of a majority in interest of the then outstanding Series C Preferred Stock; and

                           (v)      a three (3) member Compensation Committee,
one of the members of which shall be nominated by the directors elected pursuant
to subparagraph (i) above and who shall not be the Founder and one of the
members of which shall be nominated by the directors elected pursuant to
subparagraphs (ii), (iii) and (iv) above.

         Each of the parties further covenants and agrees to vote, to the extent
possible, all Shares of Stock of the Company now owned or hereafter acquired by
such party so that (i) the Company's Board of Directors shall consist of six (6)
members, each of whom shall be nominated as set forth above and (ii) the
Compensation Committee thereof shall consist of three (3) members, each of whom
shall be nominated as set forth above, (iii) the holders of the Series A
Preferred Stock, Series B Preferred Stock, Series C Preferred Stock and the
Founder's Common shall be entitled, in the aggregate, to have up to three
persons as observers at each meeting of the Board of Directors and any committee
(other than the Compensation Committee) thereof. For the purposes of this
Agreement, "Stock" shall mean and include all Preferred Stock and Common Stock
and all other securities of the Company which may be exchangeable for or issued
in exchange for or in respect of shares of Common Stock (whether by way of stock
split, stock dividends, combination, reclassification, reorganization or any
other means).

         In the absence of any designation from the persons or groups so
designating directors as specified above, the director previously designated by
them and then serving shall be reelected if still eligible to serve as provided
herein.

         No party hereto shall vote to remove any member of the Board of
Directors or the Compensation Committee thereof designated in accordance with
the aforesaid procedure unless the persons or groups so designating directors as
specified above so vote, and, if such persons or groups so vote then the
non-designating party or parties shall likewise so vote.

         Any vacancy on the Board of Directors or the Compensation Committee
thereof created by the resignation, removal, incapacity or death of any person
designated under this Section 5 shall be filled by another person designated in
a manner so as to preserve the constituency of the Board or such Committee as
provided above.

         (b) ISSUANCE OF OPTIONS TO HOLDERS OF PREFERRED STOCK. Each of the
parties hereto agrees that the Company shall not, and each agrees to vote all of
their Stock of the Company now owned or hereafter acquired by such party (and
attend, in person or by proxy, all meetings of stockholders called for the
purpose of electing directors) to preclude the Company from issuing any options
under the Company's stock option plans as in effect from time to time to any
holder of Preferred Stock or any person employed by or controlled by or under
common control

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with any such holder or any affiliate thereof without first obtaining the
unanimous approval of the Board of Directors of the Company.

         6. RIGHT OF PARTICIPATION IN SALES BY THE COMPANY.

         (a) RIGHT OF PARTICIPATION. Except as provided in Section 6(f) of this
Agreement, the Company shall not issue, sell or exchange, agree or obligate
itself to issue, sell or exchange, or reserve or set aside for issuance, sale or
exchange, any (i) shares of Common Stock, (ii) any other equity security of the
Company, including without limitation, shares of Preferred Stock, (iii) any debt
security of the Company (other than debt with no equity feature) including
without limitation, any debt security which by its terms is convertible into or
exchangeable for any equity security of the Company, (iv) any security of the
Company that is a combination of debt and equity, or (v) any option, warrant or
other right to subscribe for, purchase or otherwise acquire any such equity
security or any such debt security of the Company, unless in each case the
Company shall have first offered to sell such securities (the "Offered
Securities") to the Purchasers who hold individually or together with their
affiliates at least 2,500,000 Shares of the Preferred Stock then outstanding
and, for so long as the Founder holds not less than fifty percent (50%) of the
number of shares of Founder's Common held by him on the date hereof (in both
cases, as adjusted for stock splits, stock dividends, reclassifications,
recapitalizations or other similar events), the holders of the Founder's Common
(such Purchasers and, if applicable, the holders of the Founders' Common being
referred to as the "Participating Stockholders") as follows: The Company shall
offer to sell to each Participating Stockholder (a) that portion of the Offered
Securities as the number of shares of Common Stock (including all shares of
capital stock convertible into Common Stock, on a fully-diluted basis) then held
by such Participating Stockholder, as the case may be, bears to the total number
of shares of Common Stock (including all shares of capital stock convertible
into Common Stock, on a fully-diluted basis) of the Company then outstanding
(the "Basic Amount," and the aggregate of the Basic Amounts of all Participating
Stockholders being referred to as the "Aggregate Basic Amount"), and (b) such
additional portion of the Aggregate Basic Amount as such Participating
Stockholder shall indicate it will purchase should the other Participating
Stockholders subscribe for less than their Basic Amounts (the "Undersubscription
Amount"), at a price and on such other terms as shall have been specified by the
Company in writing delivered to such Participating Stockholder (the "Offer"),
which Offer by its terms shall remain open and irrevocable for a period of
twenty (20) days from receipt of the offer.

         (b) NOTICE OF ACCEPTANCE. Notice of each Participating Stockholder's
intention to accept, in whole or in part, any Offer made pursuant to Section
6(a) shall be evidenced by a writing signed by such Participating Stockholder
and delivered to the Company prior to the end of the 20-day period of such
offer, setting forth such of the Participating Stockholder's Basic Amount as
such Participating Stockholder elects to purchase and, if such Participating
Stockholder shall elect to purchase all of its Basic Amount, such
Undersubscription Amount as such Participating Stockholder shall elect to
purchase (the "Notice of Acceptance"). If the Basic Amounts subscribed for by
all Participating Stockholders are less than the total Aggregate Basic Amount,
then each Participating Stockholder who has set forth Undersubscription Amounts
in its Notice of Acceptance shall be entitled to purchase, in addition to the
Basic Amounts subscribed

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for, all Undersubscription Amounts it has subscribed for; PROVIDED, HOWEVER,
that should the Undersubscription Amounts subscribed for exceed the difference
between the Aggregate Basic Amount and the Basic Amounts subscribed for (the
"Available Undersubscription Amount"), each Participating Stockholder who has
subscribed for any Undersubscription Amount shall be entitled to purchase only
that portion of the Available Undersubscription Amount as the Undersubscription
Amount subscribed for by such Participating Stockholder bears to the total
Undersubscription Amounts subscribed for by all Participating Stockholders,
subject to rounding by the Board of Directors to the extent it reasonably deems
necessary.

         (c) CONDITIONS TO ACCEPTANCES AND PURCHASE.

                           (i)      PERMITTED SALES OF REFUSED SECURITIES.  If
Notices of Acceptance are not given by the Participating Stockholders in respect
of all the Aggregate Basic Amount, the Company shall have ninety (90) days from
the expiration of the period set forth in Section 6(a) to close the sale of all
or any part of such Aggregate Basic Amount as to which a Notice of Acceptance
has not been given by the Participating Stockholders (the "Refused Securities")
to the person or persons specified in the Offer, but only for cash and otherwise
in all respects upon terms and conditions, including, without limitation, unit
price and interest rates, which are no more favorable, in the aggregate, to such
other person or persons or less favorable to the Company than those set forth in
the Offer.

                           (ii)     REDUCTION IN AMOUNT OF OFFERED SECURITIES.
If the Company shall propose to sell less than all the Refused Securities (any
such sale to be in the manner and on the terms specified in Section 6(c)(i)
above), then each Participating Stockholder may, at its sole option and in its
sole discretion, reduce the number of, or other units of the Offered Securities
specified in its respective Notices of Acceptance to an amount which shall be
not less than the amount of the Offered Securities which the Participating
Stockholder elected to purchase pursuant to Section 6(b) multiplied by a
fraction, (A) the numerator of which shall be the amount of Offered Securities
which the Company actually proposes to sell, and (B) the denominator of which
shall be the amount of all Offered Securities. In the event that any
Participating Stockholder so elects to reduce the number or amount of Offered
Securities specified in its respective Notices of Acceptance, the Company may
not sell or otherwise dispose of more than the reduced amount of the Offered
Securities until such securities have again been offered to the Participating
Stockholders in accordance with Section 6(a).

                           (iii)    CLOSING.  Upon the closing, which shall
include full payment to the Company, of the sale to such other person or persons
of all or less than all the Refused Securities, the Participating Stockholders
shall purchase from the Company, and the Company shall sell to the Participating
Stockholders, the number of Offered Securities specified in the Notices of
Acceptance, as reduced pursuant to Section 6(c)(ii) if the Participating
Stockholders have so elected, upon the terms and conditions specified in the
Offer. The purchase by the Participating Stockholders of any Offered Securities
is subject in all cases to the preparation, execution and delivery by the
Company and the Participating Stockholders of a purchase agreement relating to
such Offered Securities reasonably satisfactory in form and substance to the
Participating Stockholders and their respective counsel.

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         (d) FURTHER SALE. In each case, any Offered Securities not purchased by
the Participating Stockholders or other person or persons in accordance with
Section 6(c) may not be sold or otherwise disposed of until they are again
offered to the Participating Stockholders under the procedures specified in
Sections 6(a), 6(b) and 6(c).

         (e) TERMINATION OF RIGHT OF PARTICIPATION. The rights of the
Participating Stockholders under this Section 6 shall terminate immediately
prior to the consummation of a Qualified Offering. In addition, the rights of
holders of the Founder's Common under this Section 6 shall terminate when the
Founder owns less than 50% of the shares of Founder's Common held by the Founder
on the date first above written (as adjusted for stock splits, stock dividends,
reclassifications, recapitalizations or other similar events). Upon the
termination of the rights of an individual or entity pursuant to this subsection
(e), such individual or entity shall no longer be deemed to be a "Participating
Stockholder" under this Section 6.

         (f) EXCEPTION. The rights of the Participating Stockholders under this
Section 6 shall not apply to:

                           (i)      Common Stock issued as a stock dividend to
holders of Common Stock or upon any subdivision or combination of shares of
Common Stock,

                           (ii)     shares of Series A Preferred Stock issued as
a dividend to holders of Series A Preferred Stock upon any subdivision or
combination of shares of such series of Series A Preferred Stock,

                           (iii)    shares of Series B Preferred Stock issued as
a dividend to holders of Series B Preferred Stock upon any subdivision or
combination of shares of such series of Series B Preferred Stock,

                           (iv)     shares of Series C Preferred Stock issued as
a dividend to holders of Series C Preferred Stock upon any subdivision or
combination of shares of such series of Series C Preferred Stock,

                           (v)      shares of Common Stock issued or issuable
upon conversion of the Series A, Series B and Series C Preferred Stock,

                           (vi)     up to 14,900,000 shares of Common Stock
issued or issuable pursuant to options, warrants or other rights (as adjusted
for any stock dividends, combinations, splits, recapitalizations and the like)
issued to employees, officers or directors of, or consultants or advisors to the
Corporation or any subsidiary pursuant to stock purchase or stock option plans
or other arrangements that are approved by the Board of Directors,

                           (vii)    Common Stock issued pursuant to the
acquisition of another corporation by the Company by merger (whereby the Company
owns no less than 51% of the voting power of such corporation) or purchase of
substantially all of its stock or assets, if such

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acquisition is approved by a majority of the Directors nominated by the holders
of the Preferred Stock in the manner set forth in Section 5 hereof,

                           (viii)   Common Stock offered to the public pursuant
to a registration statement filed under the Securities Act,

                           (ix)     the issuance Common Stock, or options or
warrants to purchase Common Stock, issued to financial institutions or lessors
in connection with commercial credit arrangements, equipment financings or
similar transactions, as approved by the two-thirds (2/3rds) of the then sitting
members of the Board of Directors,

                           (x)      shares of Series C Preferred Stock issued
pursuant to the Purchase Agreement, and

                           (xi)     the issuance of (X) Common Stock in
accordance with the exchange ratio set forth in the Agreement and Plan of Merger
for the acquisition of Allied Riser Communications Corporation, as amended prior
to the date hereof, and (Y) convertible debt ("Exchange Debt") in connection
with the acquisition of Allied Riser Communications Corporation issued in
exchange for or as replacement of and on substantially the same terms and
conditions as the convertible debt of Allied Riser Communications Corporation
outstanding at the time of the acquisition or the issuance of additional
convertible debt or equity as a paid-in-kind interest payment on such Exchange
Debt approved by the Board of Directors.

         (g) WAIVER. The rights of the Purchasers under this Section 6 may be
waived in any instance, on behalf of all of the Purchasers, prospectively or
retroactively, by the written agreement of the holders of a majority in interest
of the Preferred Stock owned beneficially or of record by the Purchasers. The
rights of holders of the Founder's Common under this Section 6 may be waived in
any instance, on behalf of all such holders, prospectively or retroactively, by
the written agreement of the holders of a majority of the Founder's Common then
outstanding. Upon waiver of the rights of the Purchasers or holders of Founder's
Common in accordance with this subsection (g) with respect to a particular
issuance, sale or exchange of Offered Securities, the Purchasers or such holder,
as the case may be, shall be excluded from the definition of "Participating
Stockholders" for purposes of this Section 6 with respect to such issuance, sale
or exchange.

         7. TERMINATION. This Agreement, and the respective rights and
obligations of the parties hereto, shall terminate upon the earliest to occur of
the following: (i) the completion of a Qualified Offering, provided that the
obligations of Section 9 shall survive such termination; or (ii) the sale of the
Company, whether by merger, sale, or transfer of more than ninety percent (90%)
of its capital stock, or sale of substantially all of its assets. In addition,
any Purchaser or Qualified Transferee may elect to terminate its rights and
obligations with respect to any or all of Sections 2, 3, 5 or 6 by providing
written notice of such election to the Company at any time after the Public
Company Date.

                                       10
<Page>

         8. NOTICES. All notices and other communications hereunder shall be in
writing and shall be deemed to have been given when delivered or mailed by first
class, registered or certified mail (air mail if to or from outside the United
States), return receipt requested, postage prepaid, or by internationally,
recognized overnight courier service (two business days after deposit with such
overnight courier service in the case of deliveries to non-U.S. residents), if
to each Holder at his respective address set forth on Schedule I hereto or on
the Instrument of Accession pursuant to which he became a party to this
Agreement, and if to the Purchasers, at their respective addresses set forth on
Schedule I hereto or to such other address as the addressee shall have furnished
to the other parties hereto in the manner prescribed by this Section 8.

         9. LOCK-UP AGREEMENT. Each of the Holders and the Purchasers hereby
agrees in connection with the Company's Qualified Offering, upon the request of
the principal underwriter managing the Qualified Offering of the Company, not to
sell publicly any Shares now owned or hereafter acquired by him, her or it and
subject to this Agreement (other than Shares being registered in such offering
or any shares purchased in the open market after the Company's initial public
offering) without the prior written consent of such underwriter for a period of
time (not to exceed one hundred eighty (180) days) from the consummation of such
Qualified Offering as the underwriter may specify, in all events subject to the
provisions of Section 13(f) of a certain Amended and Restated Registration
Rights Agreement dated as of the date hereof.

         10. FAILURE TO DELIVER SHARES. If a Holder becomes obligated to sell
any Shares owned by, or held for the benefit of, such Holder to the Founder, a
Purchaser or a Qualified Transferee under this Agreement and fails to deliver
such shares in accordance with the terms of this Agreement, the Founder or such
Purchaser, as applicable, may, at his or its option, in addition to all other
remedies it may have, send to the Company for the benefit of such Holder the
purchase price for such Shares as is herein specified. Thereupon, the Company
upon written notice to said Holder, (a) shall cancel on its books the
certificate(s) representing the Shares to be sold and (b) shall issue, in lieu
thereof, in the name of the Founder or such Purchaser, as applicable, a new
certificate(s) representing such Shares, and thereupon all of said Holder's
rights in and to such shares shall terminate. The Company may exercise a similar
remedy in enforcing its rights under Section 2. If a Holder transfers any shares
to the Founder or a Purchaser in violation of this Agreement, the Company may,
at the election of a majority of the disinterested members of the Board of
Directors, cancel on the books of the Company any shares of capital stock then
held by such Holder, and compel such Holder to purchase from the Founder or
Purchaser, as applicable, and any transferee a number of shares of capital stock
equal to the amount so transferred in violation of this Agreement.

         11. SPECIFIC PERFORMANCE. The rights of the parties under this
Agreement are unique and, accordingly, the parties shall, in addition to such
other remedies as may be available to any of them at law or in equity, have the
right to enforce their rights hereunder by actions for specific performance to
the extent permitted by law.

         12. LEGEND. Until this Agreement terminates in full, the certificates
representing the Shares shall bear on their face a legend indicating the
existence of the restrictions imposed hereby. After the Qualified Offering, the
Company shall not issue or deliver to any transfer

                                       11
<Page>

agent a stop transfer notice with respect to any Shares, the transfer of which
is permitted pursuant to Rule 144(k) and the Securities Act of 1933.

         13. ENTIRE AGREEMENT. This Agreement (including any and all exhibits,
schedules and other instruments contemplated thereby) constitutes the entire
agreement among the parties with respect to the subject matter hereof and
supersedes all prior agreements and understandings between them or any of them
as to such subject matter.

         14. WAIVERS AND FURTHER AGREEMENTS. Except as otherwise expressly set
forth herein, the rights of the Purchasers under this Agreement may be waived by
an instrument in writing executed and delivered by Purchasers holding at least
two-thirds in interest of the Common Stock (including shares of Common Stock
into which any shares of Preferred Stock are convertible) then held or deemed to
be held by all Purchasers; PROVIDED, HOWEVER, that the rights set forth in
SECTION 5 with respect to the designation of the Board of Directors of the
Company may not be waived without the prior written consent of the constituency
affected by such waiver, which waiver shall be obtained in a manner consistent
with, and shall require the same percentages prescribed in, SECTION 5. Any
waiver by any party of a breach of any provision of this Agreement shall not
operate or be construed as a waiver of any subsequent breach of that provision
or of any other provision hereof. Each of the parties hereto agrees to execute
all such further instruments and documents and to take all such further action
as any other party may reasonably require in order to effectuate the terms and
purposes of this Agreement. Notwithstanding the foregoing, no waiver approved in
accordance herewith shall be effective if and to the extent that such waiver
grants to any one or more Purchasers any rights more favorable than any rights
granted to all other Purchasers or otherwise treats any one or more Purchasers
differently than all other Purchasers.

         15. AMENDMENTS. Except as otherwise expressly provided herein, this
Agreement may not be amended except by an instrument in writing executed by (i)
Purchasers holding at least two-thirds in interest of the shares of Common Stock
issued or issuable to the Purchasers (including shares of Common Stock into
which any shares of Preferred Stock are convertible), (ii) the Company, (iii)
Holders holding a majority of the Shares subject to this Agreement and (iv)
holders of a majority of the Founder's Common. Notwithstanding the foregoing, no
amendment approved in accordance with clause (i) above shall be effective if and
to the extent that such amendment creates any additional affirmative obligations
to be complied with by any or all of the Purchasers unless approved by holders
of all of the Preferred Stock then outstanding.

         16. ASSIGNMENT; SUCCESSORS AND ASSIGNS. This Agreement shall be binding
upon and shall inure to the benefit of the parties hereto and their respective
heirs, executors, legal representatives, successors and permitted transferees,
except as may be expressly provided otherwise herein, AND PROVIDED, FURTHER,
that no Purchaser may transfer its rights or obligations hereunder except to a
Qualified Transferee. Notwithstanding anything contained herein to the contrary,
until the first to occur of (i) termination of this Agreement and (ii) a
Qualified Offering, any transferee of Preferred Stock shall, as a condition to
such transfer, deliver to the Company a written instrument by which such
transferee agrees to be bound by the obligations imposed

                                       12
<Page>

hereunder on holders of Preferred Stock to the same extent as if such transferee
had signed this Agreement.

         17. SEVERABILITY. In case any one or more of the provisions contained
in this Agreement shall for any reason be held to be invalid, illegal or
unenforceable in any respect, such invalidity, illegality or unenforceability
shall not affect any other provision of this Agreement and such invalid, illegal
and unenforceable provision shall be reformed and construed so that it will be
valid, legal, and enforceable to the maximum extent permitted by law.

         18. COUNTERPARTS.  This Agreement may be executed in two or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

         19. ADDITIONAL PARTIES. Prior to the Public Company Date, the Company
shall require each executive officer who shall, after the date hereof, acquire
any shares of Common Stock, or any other person (other than a Purchaser or
Qualified Transferee) who acquires in excess of one percent (1%) of the shares
of Common Stock or other equity securities of the Company then outstanding, in
each case as a condition to such acquisition, to become a party to this
Agreement by executing and delivering to the Company an Instrument of Accession
in the form of Schedule II hereto.

         20. SECTION HEADINGS.  The headings contained in this Agreement are for
reference purposes only and shall not in any way affect the meaning or
interpretation of this Agreement.

         21. GOVERNING LAW.  This Agreement shall be construed and enforced in
accordance with and governed by the laws of the State of New York.

         22. ORIGINAL STOCKHOLDERS AGREEMENT.  Upon and after the Closing (as
defined in the Purchase Agreement), the Original Stockholders Agreement shall be
terminated and of no further force and effect.

                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

                                       13
<Page>

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

                                   THE COMPANY:

                                   COGENT COMMUNICATIONS GROUP, INC.

                                   By: /s/ Dave Schaeffer
                                      -----------------------------
                                          Name: Dave Schaeffer
                                          Title: Chief Executive Officer

                                   PURCHASERS:

                                   OAK INVESTMENT PARTNERS IX,
                                   LIMITED PARTNERSHIP

                                   By:      Oak Associates IX, LLC,
                                            its General Partner

                                   By: /s/ Edward Glassmeyer
                                      -----------------------------
                                          Name:
                                          Title:

                                   OAK IX AFFILIATES FUND, LIMITED PARTNERSHIP

                                   By:      Oak IX Affiliates, LLC,
                                            its General Partner

                                   By: /s/ Edward Glassmeyer
                                      -----------------------------
                                          Name:
                                          Title:

                                   OAK IX AFFILIATES FUND-A, LIMITED PARTNERSHIP

                                   By:      Oak Associates IX, LLC,
                                            its General Partner

                                   By: /s/ Edward Glassmeyer
                                      -----------------------------
                                          Name:
                                          Title:

                                       14
<Page>

   [SIGNATURE PAGE TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT - CONTINUED]

                                   JERUSALEM VENTURE PARTNERS III, L.P.

                                   By:   Jerusalem Partners III, L.P.,
                                         its General Partner

                                   By:   Jerusalem Venture Partners Corporation,
                                         its General Partner

                                   By: /s/ Erel N. Margalit
                                      -----------------------------
                                        Name: Erel N. Margalit
                                        Title:

                                   JERUSALEM VENTURE PARTNERS III
                                   (ISRAEL), L.P.

                                   By:   Jerusalem Venture Partners III (Israel)
                                         Management Company Ltd.,
                                         its General Partner

                                   By: /s/ Erel N. Margalit
                                      -----------------------------
                                        Name: Erel N. Margalit
                                        Title:

                                   JERUSALEM VENTURE PARTNERS
                                   ENTREPRENEURS FUND III, L.P.

                                   By:   Jerusalem Partners III, L.P.,
                                         its General Partner

                                   By:   Jerusalem Venture Partners Corporation,
                                         its General Partner

                                   By: /s/ Erel N. Margalit
                                      -----------------------------
                                        Name: Erel N. Margalit
                                        Title:

                                       15
<Page>

   [SIGNATURE PAGE TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT - CONTINUED]

                                   JERUSALEM VENTURE PARTNERS IV, L.P.

                                   By:   Jerusalem Partners IV, L.P.,
                                         its General Partner

                                   By:   Jerusalem Venture Partners Corporation
                                         IV, its General Partner

                                   By: /s/ Erel N. Margalit
                                      -----------------------------
                                        Name: Erel N. Margalit
                                        Title:

                                   JERUSALEM VENTURE PARTNERS IV (Israel), L.P.

                                   By:   Jerusalem Partners IV - Venture
                                         Capital, L.P., its General Partner

                                   By:   Jerusalem Venture Partners Corporation
                                         IV,its General Partner

                                   By: /s/ Erel N. Margalit
                                      -----------------------------
                                        Name: Erel N. Margalit
                                        Title:

                                   JERUSALEM VENTURE PARTNERS IV-A, L.P.

                                   By:   Jerusalem Venture Partners IV, L.P.,
                                         its General Partner

                                   By:   Jerusalem Venture Partners Corporation
                                         IV, its General Partner

                                   By: /s/ Erel N. Margalit
                                      -----------------------------
                                        Name: Erel N. Margalit
                                        Title:

                                       16
<Page>

   [SIGNATURE PAGE TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT - CONTINUED]

                                   WORLDVIEW TECHNOLOGY
                                   PARTNERS III, L.P.

                                   By:      Worldview Capital III, L.P.,
                                            its General Partner

                                   By:      Worldview Equity I, L.L.C.,
                                            its General Partner

                                   By: /s/ James Wei
                                      -----------------------------
                                          Name: James Wei
                                          Title: Member

                                   WORLDVIEW TECHNOLOGY
                                   INTERNATIONAL III, L.P.

                                   By:      Worldview Capital III, L.P.,
                                            its General Partner

                                   By:      Worldview Equity I, L.L.C.,
                                            its General Partner

                                   By: /s/ James Wei
                                      -----------------------------
                                          Name: James Wei
                                          Title: Member

                                   WORLDVIEW STRATEGIC PARTNERS III, L.P.

                                   By:      Worldview Capital III, L.P.,
                                            its General Partner

                                   By:      Worldview Equity I, L.L.C.,
                                            its General Partner

                                   By: /s/ James Wei
                                      -----------------------------
                                          Name: James Wei
                                          Title: Member

                                   WORLDVIEW III CARRIER FUND, L.P.

                                   By:      Worldview Capital III, L.P.,
                                            its General Partner

                                   By:      Worldview Equity I, L.L.C.,
                                            its General Partner

                                   By: /s/ James Wei
                                      -----------------------------
                                          Name: James Wei
                                          Title: Member

                                       17
<Page>

   [SIGNATURE PAGE TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT - CONTINUED]

                                   BROADVIEW CAPITAL PARTNERS L.P.

                                   By:      Broadview Capital Partners
                                            Management LLC, its General Partner

                                   By: /s/ Stephen J. Bachmann
                                      -----------------------------
                                            Name:    Stephen J. Bachmann
                                            Title:   Managing Director

                                   BROADVIEW CAPITAL PARTNERS
                                   QUALIFIED PURCHASER FUND L.P.

                                   By:      Broadview Capital Partners
                                            Management LLC, its General Partner

                                   By: /s/ Stephen J. Bachmann
                                      -----------------------------
                                            Name:    Stephen J. Bachmann
                                            Title:   Managing Director

                                   BROADVIEW CAPITAL PARTNERS
                                   AFFILIATES FUND LLC

                                   By:      Broadview Capital LLC,
                                            its Manager

                                   By: /s/ Stephen J. Bachmann
                                      -----------------------------
                                            Name:    Stephen J. Bachmann
                                            Title:   Managing Director

                                       18
<Page>

   [SIGNATURE PAGE TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT - CONTINUED]

                                   BOULDER VENTURES III, L.P.

                                   By: /s/ Andrew E. Jones
                                      -----------------------------
                                          Name: Andrew E. Jones
                                          Title: General Partner

                                   BOULDER VENTURES III (ANNEX), L.P.

                                   By: /s/ Andrew E. Jones
                                      -----------------------------
                                          Name: Andrew E. Jones
                                          Title: General Partner

                                       19
<Page>

   [SIGNATURE PAGE TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT - CONTINUED]

                                   NAS PARTNERS I L.L.C.

                                   By: /s/ Randall A. Hack
                                      -----------------------------
                                          Name: Randall A. Hack
                                          Title: Member

                                   NASSAU CAPITAL PARTNERS IV L.P.

                                   By:      Nassau Capital LLC,
                                            its General Partner

                                   By: /s/ Randall A. Hack
                                      -----------------------------
                                          Name: Randall A. Hack
                                          Title: Member

                                       20
<Page>

   [SIGNATURE PAGE TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT - CONTINUED]

                                   SMALLCAP WORLD FUND, INC.

                                   By: /s/ Vincent P. Costi
                                      -----------------------------
                                          Name: Vincent P. Costi
                                          Title: Vice President

                                       21
<Page>

   [SIGNATURE PAGE TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT - CONTINUED]

                                      /s/ David Schaeffer
                                      -----------------------------
                                      David Schaeffer

                                       22
<Page>

   [SIGNATURE PAGE TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT - CONTINUED]

                                   2M TECHNOLOGY VENTURES, L.P.

                                   By:      2M Technology Group LLC,
                                            its General Partner

                                   By: /s/ A. Scott Letier
                                      -----------------------------
                                          Name: A. Scott Letier
                                          Title: Vice President

                                       23
<Page>

                                   SCHEDULE I

Dave Schaeffer
Denise Shen
Ruth E. Schaeffer, Trustee of the Schaeffer Descendents Trust
Barry Morris
Scott Welker
Thaddeus Weed
Edward Lu
Bradley Griggs
Scott Stewart
C. Blair Partners, LP
C. Blair Partners II, LP
C. Blair Fund, Ltd.

Jerusalem Venture Partners III (Israel) LP:      Jerusalem Technology Park
                                                 Building One
                                                 Mahla, Jerusalem 91847
                                                 Attn: Erel Margalit

Jerusalem Venture Partners III LP                666 Fifth Avenue
Jerusalem Venture Partners Entrepreneurs Fund    Suite 195
LP:                                              New York, NY 10103

Oak Investment Partners IX, LP                   One Gorham Island
Oak IX Affiliates Fund, LP                       Westport, CT 06880
Oak IX Affiliates Fund-A, LP                     Attn: Ed Glassmeyer

Worldview Technology Partners III, LP            435 Tasso Street #120
Worldview Technology  International III, LP      Palo Alto, CA 94301
Worldview Strategic Partners III, LP             Attn: James Wei
Worldview III Carrier Fund, LP

Boulder Ventures III, LP                         4750 Owings Mills Blvd.
Boulder Ventures III (Annex), LP                 Owings Mills, MD 21117
                                                 Attn:  Andy Jones

Comdisco, Inc.                                   3rd Floor South
                                                 Totten Pond Office Center
                                                 400-1 Totten Pond Road, Suite 5
                                                 Waltham, MA 02451
                                                 Attn: Jan Haas

                                       24
<Page>

ACON Venture Partners, LP                        345 California Street
                                                 Suite 3300
                                                 San Francisco, CA 94104
                                                 Attn: Jon Levinson

Clipperbay & Co.                                 3000 K Street. NW
                                                 Suite 230
                                                 Washington, DC 20007
                                                 Attn: Brad Vogt

Covestco-Venteura, LLC                           c/o Jura Trust
                                                 Mitteldorf 1
                                                 Vaduz, Liechtenstein, FL-9490
                                                 Attn: Albin A. Johann

Nassau Capital Partners IV, LP                   22 Chambers Street
NAS Partners I, LLC                              Princeton, NJ 08542
                                                 Attn:  Randall A. Hack
Broadview Capital Partners Qualified Purchaser   950 Tower Lane, 18th Floor
Fund LP                                          Foster City, CA  94404
Broadview Capital Partners LP                    Attn:  David Kapnick
Broadview Capital Partners Affiliates Fund LLC
Broadview BCPSBS Fund LP

2M Technology Ventures, L.P.                     3401 Armstrong Ave.
                                                 Dallas, TX  75205
                                                 Attn:  Scott Letier

Paul Johnson

Spencer Punter

Scappoose Portland, LLC

Brian Rich

Constantine Scontras

David Steinberg

<Page>

Raj Mehra

Edward Pollack

John D. Watson, Jr.

Latham & Watkins, a California general partnership

Brooke Coburn

Colin Stern

Robert Nabholz

Rafi Gidron

Robert Barron

Louis E. Martinage

R. Brad Kummer

University of Maryland Foundation for UMBC

Friedman Kaplan Seiler & Adelman LLP

Jeff Barrows

Jim Dertzbaugh

Gordon P. Griggs, Trustee, Declaration of Trust of Gordon P. Griggs

Brian Griggs and Melissa Griggs, Trustees for Griggs Family Trust

Jeffrey Allen Knepp

Kevin Pavuk

Melvin Young

Andrew Morrison

Bridget Oppenheimer

Keith Steinberg

<Page>

Samuel Parker

Kevin Gallagher

Karen Chow

Michael Van Vleck

Behdad Eghbali

Paul Hauser

Matthew Whalen

Hans Wittich

David J. Daigle

Larry Collins

John Leone

Dave Diller

William Currer

Kenneth Klamm

David Ordonio

Jeffrey Megrue

H. Helen Lee

Comdisco, Inc.

Applegreen Capital, Inc.

Clipperbay & Co.

<Page>

                                   SCHEDULE II

                        COGENT COMMUNICATIONS GROUP, INC.

                             INSTRUMENT OF ACCESSION

         The undersigned, _________________, as a condition precedent to
becoming the owner or holder of record of ___________________ (______) shares of
the Common Stock, par value $.001 per share, of Cogent Communications Group,
Inc., a Delaware corporation (the "Company"), hereby agrees to become a Holder
party to and bound by that certain Stockholders Agreement dated as of _________
___, 2001 by and among the Company and other stockholders of the Company. This
Instrument of Accession shall take effect and shall become an integral part of
the said Stockholders Agreement immediately upon execution and delivery to the
Company of this Instrument.

         IN WITNESS WHEREOF, this INSTRUMENT OF ACCESSION has been duly executed
by or on behalf of the undersigned, as a sealed instrument under the laws of the
State of Delaware, as of the date below written.

                                   Signature:

                                   --------------------------------------
                                   (Print Name)

                                   Address:

                                   Date:
                                         --------------------------------

                                   Accepted:

                                   COGENT COMMUNICATIONS GROUP , INC.

                                   By:
                                        ---------------------------------
                                     Name:
                                           ------------------------------
                                     Title:
                                            -----------------------------
                                   Date:
                                         --------------------------------<Page>
                                                                   Exhibit 4.2
                        COGENT COMMUNICATIONS GROUP, INC.

                              AMENDED AND RESTATED
                          REGISTRATION RIGHTS AGREEMENT

                                                    October 16, 2001

To Dave Schaeffer (the "Founder") and each of the several holders of Series A
Preferred Stock (the "Series A Purchasers"), Series B Preferred Stock (the
"Series B Purchasers") and Series C Preferred Stock (the "Series C Purchasers")
that are parties hereto (collectively, the "Purchasers"):

Dear Sirs:

This will confirm that in consideration of the Series C Purchasers' agreement on
the date hereof to purchase, subject to the terms and conditions set forth
therein, up to 52,137,643 shares of Series C Preferred Stock of Cogent
Communications Group, Inc. (the "Company") pursuant to the Series C
Participating Convertible Preferred Stock Purchase Agreement of even date
herewith (the "Series C Purchase Agreement") and as an inducement to the Series
C Purchasers to enter into the Series C Purchase Agreement, the Company
covenants and agrees with each of you as follows:

     1.  CERTAIN DEFINITIONS. As used in this Agreement, the following terms
shall have the following respective meanings:

         "COMMISSION" shall mean the Securities and Exchange Commission, or any
other federal agency at the time administering the Securities Act.

         "COMMON STOCK" shall mean the Common Stock, par value $.001 per share,
of the Company, as constituted as of the date of this Agreement.

         "CONVERSION SHARES" shall mean shares of Common Stock issued or
issuable upon conversion of the Preferred Stock, and any shares of capital stock
received in respect thereof.

         "EXCHANGE ACT" shall mean the Securities Exchange Act of 1934 or any
similar federal statute, and the rules and regulations of the Commission
thereunder, all as the same shall be in effect at the time.

         "FOUNDER'S COMMON" shall mean the 13,600,000 shares (appropriately
adjusted for any subdivision or combination) of Common Stock issued to the
Founder (David Schaeffer).

         "PREFERRED STOCK" shall mean the Series A Preferred Stock, the Series B
Preferred Stock and the Series C Preferred Stock.

<Page>

         "REGISTRATION EXPENSES" shall mean the expenses so described in Section
8.

         "RESTRICTED STOCK" shall mean (i) the Conversion Shares, excluding
Conversion Shares which have been (a) registered under the Securities Act
pursuant to an effective registration statement filed thereunder and disposed of
in accordance with the registration statement covering them or (b) publicly sold
pursuant to Rule 144 under the Securities Act, (ii) the Founder's Common, and
(iii) any shares of Common Stock issued or distributed in respect of the
securities described in clauses (i) and (ii).

         "SECURITIES ACT" shall mean the Securities Act of 1933 or any similar
federal statute, and the rules and regulations of the Commission thereunder, all
as the same shall be in effect at the time.

         "SELLING EXPENSES" shall mean the expenses so described in Section 8.

         "SERIES A PREFERRED STOCK" shall mean the Series A Participating
Convertible Preferred Stock, par value $.001 per share, of the Company, as
constituted as of the date of this Agreement.

         "SERIES B PREFERRED STOCK" shall mean the Series B Participating
Convertible Preferred Stock, par value $.001 per share, of the Company, as
constituted as of the date of this Agreement.

         "SERIES C PREFERRED STOCK" shall mean the Series C Participating
Convertible Preferred Stock, par value $.001 per share, of the Company, as
constituted as of the date of this Agreement.

     2.  RESTRICTIVE LEGEND. Each certificate representing Preferred Stock,
Conversion Shares or Restricted Stock shall, except as otherwise provided in
this Section 2 or in Section 3, be stamped or otherwise imprinted with a legend
substantially in the following form:

                  "The securities represented by this certificate have not been
         registered under the Securities Act of 1933 or applicable state
         securities laws. These securities have been acquired for investment and
         not with a view to distribution or resale, and may not be sold
         mortgaged, pledged, hypothecated or otherwise transferred without an
         effective registration statement for such securities under the
         Securities Act of 1933 and applicable state securities laws, or the
         availability of an exemption from the registration provisions of the
         Securities Act of 1933 and applicable state securities laws."

A certificate shall not bear such legend if in the opinion of counsel reasonably
satisfactory to the Company the securities being sold thereby may be publicly
sold

<Page>

without registration under the Securities Act.

     3.  NOTICE OF PROPOSED TRANSFER. Prior to any proposed transfer of any
Preferred Stock, Conversion Shares or Restricted Stock (other than under the
circumstances described in Sections 4, 5 or 6), the holder thereof shall give
written notice to the Company of its intention to effect such transfer. Each
such notice shall describe the manner of the proposed transfer and, if requested
by the Company, shall be accompanied by an opinion of counsel reasonably
satisfactory to the Company to the effect that the proposed transfer may be
effected without registration under the Securities Act, whereupon the holder of
such stock shall be entitled to transfer such stock in accordance with the terms
of its notice; PROVIDED, HOWEVER, that no such opinion of counsel shall be
required for a transfer to one or more partners of the transferor (in the case
of a transferor that is a partnership), to one or more members of the transferor
(in the case of a transferor that is a limited liability company) or to an
affiliated corporation (in the case of a transferor that is a corporation);
PROVIDED, FURTHER, HOWEVER, that any transferee other than a partner, member or
affiliate of the transferor shall execute and deliver to the Company a
representation letter in form reasonably satisfactory to the Company's counsel
to the effect that the transferee is acquiring Restricted Stock for its own
account, for investment purposes and without any view to distribution thereof.
Each certificate for Preferred Stock or Conversion Shares transferred as above
provided shall bear the legend set forth in Section 2, except that such
certificate shall not bear such legend if (i) such transfer is in accordance
with the provisions of Rule 144 (or any other rule permitting public sale
without registration under the Securities Act) or (ii) the opinion of counsel
referred to above is to the further effect that the transferee and any
subsequent transferee (other than an affiliate of the Company) would be entitled
to transfer such securities in a public sale without registration under the
Securities Act. The restrictions provided for in this Section 3 shall not apply
to securities which are not required to bear the legend prescribed by Section 2
in accordance with the provisions of that Section.

     4.  REQUIRED REGISTRATION.

         (a) Subject to Section 13(f) of this Agreement, at any time after
the earlier of (i) the second anniversary of the date hereof and (ii) the
date that is six (6) months after the first public offering of securities by
the Company, holders of Restricted Stock constituting more than one-third of
the total number of shares of Restricted Stock then outstanding or a lesser
percent if the anticipated offering price, net of underwriting discounts and
commissions would be at least $5,000,000, may request the Company to register
under the Securities Act all or any portion of the shares of Restricted Stock
held by such requesting holder or holders for sale in the manner specified in
such notice. For purposes of this Section 4 and Sections 5, 6, 13(a) and
13(d), the term "Restricted Stock" shall be deemed to include the number of
shares of Restricted Stock which would be issuable to a holder of Preferred
Stock upon conversion of all shares of Preferred Stock held by such holder at
such time; PROVIDED, HOWEVER, that the only securities which the Company
shall be required to register pursuant hereto shall be shares of Common
Stock; PROVIDED, FURTHER, HOWEVER, that, in any underwritten public offering
contemplated by this

<Page>

Section 4 or Sections 5 and 6, the holders of Preferred Stock shall be entitled
to sell such Preferred Stock to the underwriters for conversion and sale of the
shares of Common Stock issued upon conversion thereof and holders of a majority
of the Preferred Stock being so registered shall have the right to approve the
managing underwriter(s) selected by the Company in connection with such
underwritten public offering. In addition, shares of Founder's Common shall not
be deemed Restricted Stock for purposes of this Section 4. Notwithstanding
anything to the contrary contained herein, the Company shall not be obligated to
effect a registration (i) during the 180 day period commencing with the
effective date of a registration statement filed by the Company covering the
first firm commitment underwritten public offering after the date hereof or (ii)
if the Company delivers notice to the holders of the Restricted Stock within
thirty (30) days of any registration request of the Company's intent to file a
registration statement for an underwritten public offering within ninety (90)
days.

         (b) Following receipt of any notice under this Section 4, the Company
shall immediately notify all holders of Restricted Stock and Preferred Stock
from whom notice has not been received and such holders shall then be entitled
within 30 days thereafter to request the Company to include in the requested
registration all or any portion of their shares of Restricted Stock. The Company
shall use its best efforts to register under the Securities Act, for public sale
in accordance with the method of disposition described in paragraph (a) above,
the number of shares of Restricted Stock specified in such notice (and in all
notices received by the Company from other holders within 30 days after the
giving of such notice by the Company). The Company shall be obligated to
register Restricted Stock pursuant to this Section 4 on three occasions only;
PROVIDED, HOWEVER, that such obligation shall be deemed satisfied only when a
registration statement covering all shares of Restricted Stock specified in
notices received as aforesaid for sale in accordance with the method of
disposition specified by the requesting holders shall have become effective and,
if such method of disposition is a firm commitment underwritten public offering,
all such shares shall have been sold pursuant thereto.

         (c) The Company (or at the option of the Company, the holders of Common
Stock) shall be entitled to include in any registration statement referred to in
this Section 4, for sale in accordance with the method of disposition specified
by the requesting holders, shares of Common Stock to be sold by the Company or
such other holders for its own account, except as and to the extent that, in the
opinion of the managing underwriter (if such method of disposition shall be an
underwritten public offering), such inclusion would adversely affect the
marketing of the Restricted Stock to be sold. Subject to Section 4(a) and except
for registration statements on Form S-4, S-8 or any successor thereto, the
Company will not file with the Commission any other registration statement with
respect to its Common Stock, whether for its own account or that of other
stockholders, from the date of receipt of a notice from requesting holders
pursuant to this Section 4 until the completion of the period of distribution of
the registration contemplated thereby.

         (d) If, in the opinion of the managing underwriter, the inclusion of
all

<Page>

of the Restricted Stock requested to be registered under this Section would
adversely affect the marketing of such shares, the Company shall only include
the number of shares that, in the reasonable opinion of such underwriter, can be
sold without having an adverse effect on the marketing of such shares, to be
allocated as follows: first, to the holders of the Series C Preferred Stock (or
the shares of Common Stock issued upon conversion thereof) on a PRO RATA basis
based on the total number of shares of Restricted Stock held by such holders and
requested to be included in the registration; second, to the holders of the
Series A and Series B Preferred Stock (or the shares of Common Stock issued upon
conversion thereof) on a PRO RATA basis based on the total number of shares of
Restricted Stock held by such holders and requested to be included in the
registration; and third, to any stockholder of the Company (other than such
holders) on a PRO RATA basis based on the total number of shares held by such
holder and requested to be included in the registration; provided however that
the number of shares of Restricted Stock to be included in such underwriting and
registration shall not be reduced unless all other securities of the Company are
first excluded from the underwriting and registration.

     5.  INCIDENTAL REGISTRATION. Subject to Section 13(f) of this Agreement, if
the Company at any time (other than pursuant to Section 4 or Section 6) proposes
to register any of its securities under the Securities Act for sale to the
public, whether for its own account or for the account of other security holders
or both (except with respect to registration statements on Forms S-4, S-8 or
another form not available for registering the Restricted Stock for sale to the
public), each such time it will give written notice to all holders of
outstanding Restricted Stock of its intention so to do. Upon the written request
of any such holder, received by the Company within 30 days after the giving of
any such notice by the Company, to register any of its Restricted Stock, the
Company will use its best efforts to cause the Restricted Stock as to which
registration shall have been so requested to be included in the securities to be
covered by the registration statement proposed to be filed by the Company, all
to the extent requisite to permit the sale or other disposition by the holder
(in accordance with its written request) of such Restricted Stock so registered.
In the event that any registration pursuant to this Section 5 shall be, in whole
or in part, an underwritten public offering of Common Stock, if the managing
underwriter determines in good faith that marketing factors require a limitation
of the number of shares to be underwritten, the number of shares that may be
included in the underwriting shall be allocated, first, to the Company; second,
to the holders of Restricted Stock invoking the rights under this Section 5 on a
PRO RATA basis based on the total number of shares of Restricted Stock held by
such holders; and third, to any stockholder of the Company (other than such
holders) on a PRO RATA basis. No such reduction shall reduce the amount of
securities of the selling holders included in the registration below thirty
percent (30%) of the total amount of securities included in such registration.
Furthermore, unless such offering is the Company's first underwritten public
offering of its Common Stock after the date hereof, in the event of a reduction
in the total amount of shares included in the registration, the number of shares
of Series A and Series B Preferred Stock (or the shares of Common Stock issued
upon conversion thereof) shall be reduced prior to any reduction in the number
of shares of Series C Preferred Stock (or the shares of Common Stock issued upon
conversion thereof). In no event will shares of any other selling stockholder be
included in such registration that would reduce the number of

<Page>

shares which may be included by holders of Restricted Stock without the written
consent of the holders of not less than sixty-six and two-thirds percent (66
2/3%) of the Restricted Stock proposed to be sold in the offering. If any such
holder disapproves of the terms of any such underwriting, such holder may elect
to withdraw therefrom by written notice to the Company and the underwriter,
delivered at least ten (10) business days prior to the effective date of the
registration statement. Any shares of Restricted Stock excluded or withdrawn
from such underwriting shall be excluded and withdrawn from the registration.
For any holder which is a partnership or corporation, the partners, retired
partners and stockholders of such holder, or the estates and family members of
any such partners and retired partners and any trusts for the benefit of any of
the foregoing person shall be deemed to be a single holder, and any PRO RATA
reduction with respect to such holder shall be based upon the aggregate amount
of shares carrying registration rights owned by all entities and individuals
included in such holder, as defined in this sentence. Notwithstanding the
foregoing provisions, the Company may withdraw any registration statement
referred to in this Section 5 without thereby incurring any liability to the
holders of Restricted Stock.

     6.  REGISTRATION ON FORM S-3. Subject to Section 13(f) of this Agreement,
if at any time (i) a holder or holders of Restricted Stock then outstanding
request that the Company file a registration statement on Form S-3 or any
successor thereto for a public offering of all or any portion of the shares of
Restricted Stock held by such requesting holder or holders, and (ii) the Company
is a registrant entitled to use Form S-3 or any successor thereto to register
such shares, then the Company shall use its best efforts to register under the
Securities Act on Form S-3 or any successor thereto for public sale in
accordance with the method of disposition specified in such notice, the number
of shares of Restricted Stock specified in such notice. Whenever the Company is
required by this Section 6 to use its best efforts to effect the registration of
Restricted Stock, each of the procedures and requirements of Section 4
(including but not limited to the requirement that the Company notify all
holders of Restricted Stock from whom notice has not been received and provide
them with the opportunity to participate in the offering) shall apply to such
registration; PROVIDED, HOWEVER, that there shall be no limitation on the number
of registrations on Form S-3 which may be requested and obtained under this
Section 6 and registrations effected pursuant to this Section 6 shall not be
counted as demands for registration or registrations effected pursuant to
Sections 4 or 5, respectively.

         (b) Notwithstanding anything to the contrary set forth in this
Agreement, the Company's obligation under this Agreement to register Restricted
Stock under the Securities Act on registration statements ("Registration
Statements") may, upon the reasonable determination of the Board of Directors
made not more than twice in the aggregate (and not more than once with respect
to a Registration Statement on Form S-1 and not more than once with respect to a
Registration Statement on Form S-3 and including any delay pursuant to the last
sentence of Section 4(a)) during any 12-month period, be suspended in the event
and during such period as unforeseen circumstances (including without limitation
(i) an underwritten primary offering by the Company (which includes no secondary
offering) if the Company is advised in writing by its underwriters that the
registration of the Restricted Stock would have a material adverse

<Page>

effect on the Company's offering, or (ii) pending negotiations relating to, or
consummation of, a transaction or the occurrence of an event which would require
additional disclosure of material information by the Company in Registration
Statements or such other filings, as to which the Company has a bona fide
business purpose for preserving confidentiality or which renders the Company
unable to comply with the Commission's requirements) exist (such unforeseen
circumstances being hereinafter referred to as a "Suspension Event") which would
make it impractical or unadvisable for the Company to file the Registration
Statements or such other filings or to cause such to become effective. Such
suspension shall continue only for so long as such event is continuing but in no
event for a period longer than (i) one hundred and twenty (120) days, in the
case of a Registration Statement on Form S-1 (or any successor thereto) or (ii)
ninety (90) days, in the case of a Registration Statement on Form S-3 (or any
successor thereto). The Company shall notify the Purchasers of the existence and
nature of any Suspension Event.

     7.  REGISTRATION PROCEDURES. If and whenever the Company is required by
the provisions of Sections 4, 5 or 6 to use its best efforts to effect the
registration of any shares of Restricted Stock under the Securities Act, the
Company will, as expeditiously as possible:

         (a) prepare and file with the Commission a registration statement
(which, in the case of an underwritten public offering pursuant to Section 4,
shall be on Form S-1 or other form of general applicability satisfactory to the
managing underwriter selected as therein provided) with respect to such
securities and use its best efforts to cause such registration statement to
become and remain effective for the period of the distribution contemplated
thereby (determined as hereinafter provided);

         (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 for
the period specified in paragraph (a) above and comply with the provisions of
the Securities Act with respect to the disposition of all Restricted Stock
covered by such registration statement in accordance with the sellers' intended
method of disposition set forth in such registration statement for such period;

         (c) furnish to each seller of Restricted Stock and to each underwriter
such number of copies of the registration statement and each such amendment and
supplement thereto (in each case including all exhibits) and the prospectus
included therein (including each preliminary prospectus) as such persons
reasonably may request in order to facilitate the public sale or other
disposition of the Restricted Stock covered by such registration statement;

         (d) use its best efforts to register or qualify the Restricted Stock
covered by such registration statement under the securities or "blue sky" laws
of such jurisdictions as the sellers of Restricted Stock or, in the case of an
underwritten public offering, the managing underwriter reasonably shall request;
PROVIDED, HOWEVER, that the

<Page>

Company shall not for any such purpose be required to qualify generally to
transact business as a foreign corporation in any jurisdiction where it is not
so qualified or to consent to general service of process in any such
jurisdiction;

         (e) use its best efforts to list the Restricted Stock covered by such
registration statement with any securities exchange on which the Common Stock of
the Company is then listed;

         (f) immediately notify each seller of Restricted Stock and each
underwriter under such registration statement, at any time when a prospectus
relating thereto is required to be delivered under the Securities Act, of the
happening of any event of which the Company has knowledge as a result of which
the prospectus contained in such registration statement, as then in effect,
includes an untrue statement of a material fact or omits to state a material
fact required to be stated therein or necessary to make the statements therein
not misleading in light of the circumstances then existing, and promptly prepare
and furnish to such seller a reasonable number of copies of a prospectus
supplemented or amended so that, as thereafter delivered to the purchasers of
such Restricted Stock, such prospectus shall not include an untrue statement of
a material fact or omit to state a material fact required to be stated therein
or necessary to make the statements therein not misleading in light of the
circumstances then existing;

         (g) if the offering is underwritten and at the request of any seller of
Restricted Stock, use its best efforts to furnish on the date that Restricted
Stock is delivered to the underwriters for sale pursuant to such registration:
(i) an opinion dated such date of counsel representing the Company for the
purposes of such registration, addressed to the underwriters and to such seller,
to such effect as reasonably may be requested by counsel for the underwriters,
and (ii) a letter dated such date from the independent public accountants
retained by the Company, addressed to the underwriters and to such seller,
stating that they are independent public accountants within the meaning of the
Securities Act and that, in the opinion of such accountants, the financial
statements of the Company included in the registration statement or the
prospectus, or any amendment or supplement thereof, comply as to form in all
material respects with the applicable accounting requirements of the Securities
Act, and such letter shall additionally cover such other financial matters
(including information as to the period ending no more than five business days
prior to the date of such letter) with respect to such registration as such
underwriters reasonably may request;

         (h) make available for inspection by each seller of Restricted Stock,
any underwriter participating in any distribution pursuant to such registration
statement, and any attorney, accountant or other agent retained by such seller
or underwriter, reasonable access to all financial and other records, pertinent
corporate documents and properties of the Company, as such parties may
reasonably request, and cause the Company's officers, directors and employees to
supply all information reasonably requested by any such seller, underwriter,
attorney, accountant or agent in connection with such registration statement;

<Page>

         (i) cooperate with the selling holders of Restricted Stock and the
managing underwriters, if any, to facilitate the timely preparation and delivery
of certificates representing Restricted Stock to be sold, such certificates to
be in such denominations and registered in such names as such holders or the
managing underwriters may request at least two business days prior to any sale
of Restricted Stock; and

         (j) permit any holder of Restricted Stock which holder, in the sole and
exclusive judgment, exercised in good faith, of such holder, might be deemed to
be a controlling person of the Company, to participate in good faith in the
preparation of such registration or comparable statement and to require the
insertion therein of material, furnished to the Company in writing, which in the
reasonable judgment of such holder and its counsel should be included and to
permit any other holder of Restricted Stock participating in the registration to
review such registration or comparable statement during its preparation.

         For purposes of Section 7(a) and 7(b) and of Section 4(c), the period
of distribution of Restricted Stock in a firm commitment underwritten public
offering shall be deemed to extend until each underwriter has completed the
distribution of all securities purchased by it, and the period of distribution
of Restricted Stock in any other registration shall be deemed to extend until
the earlier of the sale of all Restricted Stock covered thereby and 180 days
after the effective date thereof.

         In connection with each registration hereunder, the sellers of
Restricted Stock will furnish to the Company in writing such information
requested by the Company with respect to themselves and the proposed
distribution by them as reasonably shall be necessary in order to assure
compliance with federal and applicable state securities laws and to make the
registration statement correct, accurate and complete in all respects with
respect to such sellers; PROVIDED, HOWEVER, that this requirement shall not be
deemed to limit any disclosure obligation arising out of any seller's
relationship to the Company if one of such seller's agents or affiliates is an
officer, director or control person of the Company. In addition, the sellers
shall, if requested by the Company, execute such other agreements, which are
reasonably satisfactory to them and which shall contain such provisions as may
be customary and reasonable in order to accomplish the registration of the
Restricted Stock.

         In connection with each registration pursuant to Sections 4, 5 or 6
covering an underwritten public offering, the Company and each seller agree to
enter into a written agreement with the managing underwriter selected in the
manner herein provided in such form and containing such provisions as are
customary in the securities business for such an arrangement between such
underwriter and companies of the Company's size and investment stature.

     8.  EXPENSES. All expenses incurred by the Company in complying with
Sections 4, 5 and 6, including, without limitation, all registration and filing
fees, printing expenses, fees and disbursements of counsel and independent
public accountants for the

<Page>

Company, fees and expenses (including counsel fees) incurred in connection with
complying with state securities or "blue sky" laws, fees and expenses of one
counsel for the selling holders of Restricted Stock in connection with the
registration of Restricted Stock, fees of the National Association of Securities
Dealers, Inc., transfer taxes, fees of transfer agents and registrars, costs of
any insurance which might be obtained, but excluding any Selling Expenses, are
called "Registration Expenses." All underwriting discounts and selling
commissions applicable to the sale of Restricted Stock and the fees and expenses
of more than one counsel for the selling holders of Restricted Stock in
connection with the registration of Restricted Stock are called "Selling
Expenses."

         The Company will pay all Registration Expenses in connection with each
registration statement under Sections 4, 5 or 6. All Selling Expenses in
connection with each registration statement under Sections 4, 5 or 6 shall be
borne by the participating sellers in proportion to the number of shares sold by
each, or by such participating sellers other than the Company (except to the
extent the Company shall be a seller) as they may agree.

     9.  INDEMNIFICATION.

         (a) To the extent permitted by law, in the event of a registration of
any of the Restricted Stock under the Securities Act pursuant to Sections 4, 5
or 6, the Company will indemnify and hold harmless each holder of Restricted
Stock, its partners, members, officers and directors, each underwriter of such
Restricted Stock thereunder and each other person, if any, who controls such
seller or underwriter within the meaning of the Securities Act, against any
losses, claims, damages or liabilities, joint or several, to which such holder,
officer, director, underwriter or controlling person may become subject under
the Securities Act, Exchange Act or otherwise, insofar as such losses, claims,
damages or liabilities (or actions in respect thereof) arise out of or are based
upon (i) any untrue statement or alleged untrue statement of any material fact
contained in any registration statement under which such Restricted Stock was
registered under the Securities Act pursuant to Sections 4, 5 or 6, any
preliminary prospectus (but only to the extent not corrected in the final
prospectus) or final prospectus contained therein, or any amendment or
supplement thereof, (ii) any blue sky application or other document executed by
the Company specifically for that purpose or based upon written information
furnished by the Company filed in any state or other jurisdiction in order to
qualify any or all of the Restricted Stock under the securities laws thereof
(any such application, document or information herein called a "Blue Sky
Application"), (iii) the omission or alleged omission to state therein a
material fact required to be stated therein or necessary to make the statements
therein not misleading, (iv) any violation by the Company or its agents of any
rule or regulation promulgated under the Securities Act or Exchange Act
applicable to the Company or its agents and relating to action or inaction
required of the Company in connection with such registration, or (v) any failure
to register or qualify the Restricted Stock in any state where the Company or
its agents has affirmatively undertaken or agreed in writing that the Company
(the undertaking of any underwriter chosen by the Company being attributed to
the Company) will undertake such registration or qualification on the seller's
behalf (provided that in such instance the

<Page>

Company shall not be so liable if it has undertaken its best efforts to so
register or qualify the Restricted Stock) and will reimburse each such holder,
and such partner, member, officer and director, each such underwriter and each
such controlling person for any legal or other expenses reasonably incurred by
them in connection with investigating or defending any such loss, claim, damage,
liability or action; PROVIDED, HOWEVER, that the Company will not be liable in
any such case if and to the extent that any such loss, claim, damage or
liability arises out of or is based upon an untrue statement or alleged untrue
statement or omission or alleged omission so made in conformity with information
furnished by any such seller, any such underwriter or any such controlling
person in writing specifically for use in such registration statement,
prospectus or Blue Sky Application.

         (b) To the extent permitted by law, in the event of a registration of
any of the Restricted Stock under the Securities Act pursuant to Sections 4, 5
or 6, each seller of such Restricted Stock thereunder, severally and not
jointly, will indemnify and hold harmless the Company, each person, if any, who
controls the Company within the meaning of the Securities Act, each officer of
the Company who signs the registration statement, each director of the Company,
each other holder of Restricted Stock, each underwriter and each person who
controls any underwriter within the meaning of the Securities Act, against all
losses, claims, damages or liabilities, joint or several, to which the Company
or such officer, director, other seller, underwriter or controlling person may
become subject under the Securities Act, Exchange Act or otherwise, insofar as
such losses, claims, damages or liabilities (or actions in respect thereof)
arise out of or are based upon any untrue statement or alleged untrue statement
of any material fact contained in the registration statement under which such
Restricted Stock was registered under the Securities Act pursuant to Sections 4,
5 or 6, any preliminary prospectus (but only to the extent not corrected in the
final prospectus) or final prospectus contained therein, or any amendment or
supplement thereof, or any Blue Sky Application or arise out of or are based
upon the omission or alleged omission to state therein a material fact required
to be stated therein or necessary to make the statements therein not misleading,
and will reimburse the Company and each such officer, director, other seller,
underwriter and controlling person for any legal or other expenses reasonably
incurred by them in connection with investigating or defending any such loss,
claim, damage, liability or action; PROVIDED, HOWEVER, that such seller will be
liable hereunder in any such case if and only to the extent that any such loss,
claim, damage or liability arises out of or is based upon an untrue statement or
alleged untrue statement or omission or alleged omission made in reliance upon
and in conformity with information pertaining to such seller, as such, furnished
in writing to the Company by such seller specifically for use in such
registration statement, prospectus or Blue Sky Application; and PROVIDED,
FURTHER, HOWEVER, that the liability of each seller hereunder shall be limited
to the proportion of any such loss, claim, damage, liability or expense which is
equal to the proportion that the public offering price of the shares sold by
such seller under such registration statement bears to the total public offering
price of all securities sold thereunder, but not in any event to exceed the net
proceeds received by such seller from the sale of Restricted Stock covered by
such registration statement.

<Page>

         (c) Promptly after receipt by an indemnified party hereunder of notice
of the commencement of any action, such indemnified party shall, if a claim in
respect thereof is to be made against the indemnifying party hereunder, notify
the indemnifying party in writing thereof, but the omission so to notify the
indemnifying party shall not relieve it from any liability which it may have to
such indemnified party other than under this Section 9 and shall only relieve it
from any liability which it may have to such indemnified party under this
Section 9 if and to the extent the indemnifying party is prejudiced by such
omission. In case any such action shall be brought against any indemnified party
and it shall notify the indemnifying party of the commencement thereof, the
indemnifying party shall be entitled to participate in and, to the extent it
shall wish, to assume and undertake the defense thereof with counsel
satisfactory to such indemnified party, and, after notice from the indemnifying
party to such indemnified party of its election so to assume and undertake the
defense thereof, the indemnifying party shall not be liable to such indemnified
party under this Section 9 for any legal expenses subsequently incurred by such
indemnified party in connection with the defense thereof other than reasonable
costs of investigation and of liaison with counsel so selected; PROVIDED,
HOWEVER, that, if the defendants in any such action include both the indemnified
party and the indemnifying party and the indemnified party shall have reasonably
concluded that the interests of the indemnified party reasonably may be deemed
to conflict with the interests of the indemnifying party, the indemnified party
shall have the right to select a separate counsel and to assume such legal
defenses and otherwise to participate in the defense of such action, with the
expenses and fees of such separate counsel and other expenses related to such
participation to be reimbursed by the indemnifying party as incurred. 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 of such claim or litigation, and no
indemnified party shall consent to entry of any judgment or settle such claim or
litigation without the prior written consent of the indemnifying party, which
consent shall not be unreasonably withheld.

         (d) If the indemnification provided for in this Section 9 is held by a
court of competent jurisdiction to be unavailable to an indemnified party with
respect to any losses, claims, damages or liabilities referred to herein, the
indemnifying party, in lieu of indemnifying such indemnified party thereunder,
shall to the extent permitted by applicable law contribute to the amount paid or
payable by such indemnified party as a result of such loss, claim, damage or
liability in such proportion as is appropriate to reflect the relative fault of
the indemnifying party on the one hand and of the indemnified party on the other
in connection with the violation that resulted in such loss, claim, damage or
liability, as well as any other relevant equitable considerations. The relative
fault of the indemnifying party and of the indemnified party shall be determined
by a court of law by reference to, among other things, whether the untrue or
alleged untrue statement of a material fact or the omission or alleged 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

<Page>

prevent such statement or omission; PROVIDED, HOWEVER, that in no event shall
any contribution by a holder of Restricted Stock hereunder exceed the net
proceeds from the offering received by such holder.

         (e) The obligations of the Company and holders of Restricted Stock
under this Section 9 shall survive completion of any offering of Restricted
Stock by a registration statement and the termination of this Agreement.

     10. CHANGES IN COMMON STOCK, SERIES A PREFERRED STOCK, SERIES B PREFERRED
STOCK OR SERIES C PREFERRED STOCK. If, and as often as, there is any change in
the Common Stock, the Series A Preferred Stock, the Series B Preferred Stock or
the Series C Preferred Stock by way of a stock split, stock dividend,
combination or reclassification, or through a merger, consolidation,
reorganization or recapitalization, or by any other means, appropriate
adjustment shall be made in the provisions hereof so that the rights and
privileges granted hereby shall continue with respect to the Common Stock, the
Series A Preferred Stock, the Series B Preferred Stock or the Series C Preferred
Stock as so changed.

     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 Restricted Stock to the public without registration, at all times
after 90 days after any registration statement covering a public offering of
securities of the Company under the Securities Act shall have become effective,
the Company agrees to:

         (a) make and keep public information available, as those terms are
understood and defined in Rule 144 under the Securities Act;

         (b) use its best efforts to file with the Commission in a timely manner
all reports and other documents required of the Company under the Securities Act
and the Exchange Act; and

         (c) furnish to each holder of Restricted Stock forthwith upon request a
written statement by the Company as to its compliance with the reporting
requirements of such Rule 144 and of the Securities Act and the Exchange Act, a
copy of the most recent annual or quarterly report of the Company, and such
other reports and documents so filed by the Company as such holder may
reasonably request in availing itself of any rule or regulation of the
Commission allowing such holder to sell any Restricted Stock without
registration.

     12. REPRESENTATIONS AND WARRANTIES OF THE COMPANY. The Company represents
and warrants to you as follows:

         (a) The execution, delivery and performance of this Agreement by the
Company have been duly authorized by all requisite corporate action and will not
violate any provision of law, any order of any court or other agency of
government, the articles of organization or By-laws of the Company or any
provision of any indenture, agreement

<Page>

or other instrument to which it or any or its properties or assets is bound,
conflict with, result in a breach of or constitute (with due notice or lapse of
time or both) a default under any such indenture, agreement or other instrument
or result in the creation or imposition of any lien, charge or encumbrance of
any nature whatsoever upon any of the properties or assets of the Company.

         (b) This Agreement has been duly executed and delivered by the Company
and constitutes the legal, valid and binding obligation of the Company,
enforceable in accordance with its terms.

     13. MISCELLANEOUS.

         (a) All covenants and agreements contained in this Agreement by or on
behalf of any of the parties hereto shall bind and inure to the benefit of the
respective successors and assigns of the parties hereto (including without
limitation transferees of any Preferred Stock or Restricted Stock), whether so
expressed or not; PROVIDED, HOWEVER, that registration rights conferred herein
on the holders of Preferred Stock or Restricted Stock shall only inure to the
benefit of a transferee of Preferred Stock or Restricted Stock if (i) there is
transferred to such transferee at least twenty five percent (25%) of the shares
of Restricted Stock (appropriately adjusted for any subdivision or combination)
originally issued to a Purchaser, (ii) such transferee is a member, former
member, partner, retired partner, family member or trust for the benefit of any
individual holder, stockholder or affiliate of a party hereto or (iii) such
transferee acquires at least 2,500,000 shares (appropriately adjusted for any
subdivision or combination) of Preferred Stock; PROVIDED, FURTHER, HOWEVER, that
the Company is given written notice thereof.

         (b) All notices, requests, consents and other communications hereunder
shall be in writing and shall be mailed by certified or registered mail, return
receipt requested, postage prepaid, or by recognized overnight delivery service
of international reputation or, in the case of non-U.S. residents, telexed or
sent by recognized overnight delivery service of international reputation or,
addressed as follows:

         if to the Company or any other party hereto, at the address of such
party set forth in the Series C Purchase Agreement, as the case may be, or in
that certain Stockholders Agreement by and among the parties hereto dated as of
the date hereof with a copy to the Company's counsel as indicated therein;

         if to any subsequent holder of Preferred Stock or Restricted Stock,
to it at such address as may have been furnished to the Company in writing by
such holder;

or, in any case, at such other address or addresses as shall have been furnished
in writing to the Company (in the case of a holder of Preferred Stock or
Restricted Stock) or to the holders of Preferred Stock or Restricted Stock (in
the case of the Company) in accordance with the provisions of this paragraph.

         (c) This Agreement shall be construed and enforced in accordance

<Page>

with and governed by the laws of the State of New York.

         (d) This Agreement may not be amended or modified, and no provision
hereof may be waived, without the written consent of the Company and the holders
of at least two-thirds of the outstanding shares of Restricted Stock.
Notwithstanding the foregoing, no such amendment or modification shall be
effective if and to the extent that such amendment or modification either (a)
creates any additional affirmative obligations to be complied with by any or all
of the Purchasers or (b) grants to any one or more Purchasers any rights more
favorable than any rights granted to all other Purchasers or otherwise treats
any one or more Purchasers differently than all other Purchasers.

         (e) This Agreement may be executed in two or more counterparts, each of
which shall be deemed an original, but all of which together shall constitute
one and the same instrument.

         (f) If requested in writing by the underwriters for the first
underwritten public offering of securities of the Company after the date hereof,
each holder of Restricted Stock who is a party to this Agreement shall agree not
to sell publicly any shares of Restricted Stock or any other shares of Common
Stock (other than shares of Restricted Stock or other shares of Common Stock
being registered in such offering or any shares purchased in the open market
after the Company's public offering), without the consent of such underwriters,
for a period of not more than 180 days following the consummation of such public
offering; PROVIDED, HOWEVER, that all holders of at least one percent (1%) of
the then outstanding Common Stock and all officers and directors of the Company
shall also have agreed not to sell publicly their Common Stock under the
circumstances and pursuant to the terms set forth in this Section 13(f).

         (g) If any provision of this Agreement shall be held to be illegal,
invalid or unenforceable, such illegality, invalidity or unenforceability shall
attach only to such provision and shall not in any manner affect or render
illegal, invalid or unenforceable any other provision of this Agreement, and
this Agreement shall be carried out as if any such illegal, invalid or
unenforceable provision were not contained herein.

         (h) Upon and after the Closing (as defined in the Series C Purchase
Agreement), this Agreement shall amend and restate in its entirety the
Registration Rights Agreement, dated March 14, 2001, by and among the Company,
the Founder and the other parties thereto, the parties hereto constitute the
Company and the holders of at least two-thirds of the outstanding shares of
Restricted Stock immediately prior to the execution of this Agreement.

         (i) After the date of this Agreement, the Company shall not, without
the prior written consent of the holders of at least sixty-six and two-thirds
percent (66- 2/3%) of the Restricted Stock then outstanding, enter into any
agreement with any holder or prospective holder of any securities of the Company
that would grant such holder registration rights pari passu or senior to those
granted to the holders hereunder, other

<Page>

than (i) with respect to any warrants issued to Cisco Systems Capital
Corporation or its affiliates in connection with the Company's increase of its
credit facility with Cisco Systems or (ii) a registration related to stock
issued upon conversion of debt securities assumed by the Company in connection
with its acquisition of Allied Riser Communications Corporation.

         (j) All registration rights granted under Sections 4, 5, and 6 shall
terminate and be of no further force and effect upon the earlier of (i) three
(3) years after the date the Company first effects a registration pursuant to
Section 4 or (ii) five (5) years from the date hereof. In addition, the
registration rights of a holder of Restricted Stock shall expire if all
Restricted Stock held by and issuable to such holder (and its affiliates) may be
sold under Rule 144 during any ninety (90) day period.

                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

<Page>

         Please indicate your acceptance of the foregoing by signing and
returning the enclosed counterpart of this letter, whereupon this Agreement
shall be a binding agreement between the Company and you.

                                   Very truly yours,

                                   COGENT COMMUNICATIONS GROUP, INC.

                                   By: /s/ Dave Schaeffer
                                      ----------------------------------
                                       Name: Dave Schaeffer
                                       Title: Chief Executive Officer

                                   PURCHASERS:

                                   OAK INVESTMENT PARTNERS IX,
                                   LIMITED PARTNERSHIP

                                   By:   Oak Associates IX, LLC,
                                         its General Partner

                                   By: /s/ Edward F. Glassmeyer
                                       ----------------------------------
                                       Name:
                                       Title:

                                   OAK IX AFFILIATES FUND, LIMITED PARTNERSHIP

                                   By:   Oak IX Affiliates, LLC,
                                         its General Partner

                                   By: /s/ Edward F. Glassmeyer
                                       ----------------------------------
                                       Name:
                                       Title:

                                   OAK IX AFFILIATES FUND-A, LIMITED PARTNERSHIP

                                   By:   Oak Associates IX, LLC,
                                         its General Partner

                                   By: /s/ Edward F. Glassmeyer
                                       ----------------------------------
                                       Name:
                                       Title:

<Page>

          [SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT - CONTINUED]

                                   JERUSALEM VENTURE PARTNERS III, L.P.

                                   By:   Jerusalem Partners III, L.P.,
                                         its General Partner

                                   By:   Jerusalem Venture Partners Corporation,
                                         its General Partner

                                   By: /s/ Erel N. Margalit
                                       ----------------------------------
                                       Name: Erel N. Margalit
                                       Title:

                                   JERUSALEM VENTURE PARTNERS III
                                   (ISRAEL), L.P.

                                   By:   Jerusalem Venture Partners III (Israel)
                                         Management Company Ltd.,
                                         its General Partner

                                   By: /s/ Erel N. Margalit
                                       ----------------------------------
                                       Name: Erel N. Margalit
                                       Title:

                                   JERUSALEM VENTURE PARTNERS
                                   ENTREPRENEURS FUND III, L.P.

                                   By:   Jerusalem Partners III, L.P.,
                                         its General Partner

                                   By:   Jerusalem Venture Partners Corporation,
                                         its General Partner

                                   By: /s/ Erel N. Margalit
                                       ----------------------------------
                                       Name: Erel N. Margalit
                                       Title:

<Page>

          [SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT - CONTINUED]

                                   JERUSALEM VENTURE PARTNERS IV, L.P.

                                   By:   Jerusalem Partners IV, L.P.,
                                         its General Partner

                                   By:   Jerusalem Venture Partners Corporation
                                         IV, its General Partner

                                   By: /s/ Erel N. Margalit
                                       ----------------------------------
                                       Name: Erel N. Margalit
                                       Title:

                                   JERUSALEM VENTURE PARTNERS IV (Israel), L.P.

                                   By:   Jerusalem Partners IV - Venture
                                         Capital, L.P., its General Partner

                                   By:   Jerusalem Venture Partners Corporation
                                         IV,its General Partner

                                   By: /s/ Erel N. Margalit
                                       ----------------------------------
                                       Name: Erel N. Margalit
                                       Title:

                                   JERUSALEM VENTURE PARTNERS IV-A, L.P.

                                   By:   Jerusalem Venture Partners IV, L.P.,
                                         its General Partner

                                   By:   Jerusalem Venture Partners Corporation
                                         IV, its General Partner

                                   By: /s/ Erel N. Margalit
                                       ----------------------------------
                                       Name: Erel N. Margalit
                                       Title:

<Page>

          [SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT - CONTINUED]

                                   WORLDVIEW TECHNOLOGY
                                   PARTNERS III, L.P.

                                   By:   Worldview Capital III, L.P.,
                                         its General Partner

                                   By:   Worldview Equity I, L.L.C.,
                                         its General Partner

                                   By: /s/ James Wei
                                       ----------------------------------
                                       Name: James Wei
                                       Title: Member

                                   WORLDVIEW TECHNOLOGY
                                   INTERNATIONAL III, L.P.

                                   By:   Worldview Capital III, L.P.,
                                         its General Partner

                                   By:   Worldview Equity I, L.L.C.,
                                         its General Partner

                                   By: /s/ James Wei
                                       ----------------------------------
                                       Name: James Wei
                                       Title: Member

                                   WORLDVIEW STRATEGIC PARTNERS III, L.P.

                                   By:   Worldview Capital III, L.P.,
                                         its General Partner

                                   By:   Worldview Equity I, L.L.C.,
                                         its General Partner

                                   By: /s/ James Wei
                                       ----------------------------------
                                       Name: James Wei
                                       Title: Member

                                   WORLDVIEW III CARRIER FUND, L.P.

                                   By:   Worldview Capital III, L.P.,
                                         its General Partner

                                   By:   Worldview Equity I, L.L.C.,
                                         its General Partner

                                   By:/s/ James Wei
                                       ----------------------------------
                                       Name: James Wei
                                       Title: Member

<Page>

          [SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT - CONTINUED]

                                   BROADVIEW CAPITAL PARTNERS L.P.

                                   By:   Broadview Capital Partners
                                         Management LLC, its General Partner

                                   By: /s/ Stephen J. Bachmann
                                       ----------------------------------
                                       Name:    Stephen J. Bachmann
                                       Title:   Managing Director

                                   BROADVIEW CAPITAL PARTNERS
                                   QUALIFIED PURCHASER FUND L.P.

                                   By:   Broadview Capital Partners
                                         Management LLC, its General Partner

                                   By: /s/ Stephen J. Bachmann
                                       ----------------------------------
                                       Name:    Stephen J. Bachmann
                                       Title:   Managing Director

                                   BROADVIEW CAPITAL PARTNERS
                                   AFFILIATES FUND LLC

                                   By:   Broadview Capital LLC,
                                         its Manager

                                   By: /s/ Stephen J. Bachmann
                                       ----------------------------------
                                       Name:    Stephen J. Bachmann
                                       Title:   Managing Director

<Page>

          [SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT - CONTINUED]

                                   BOULDER VENTURES III, L.P.

                                   By: /s/ Andrew E. Jones
                                       ----------------------------------
                                       Name: Andrew E. Jones
                                       Title: General Partner

                                   BOULDER VENTURES III (ANNEX), L.P.

                                   By: /s/ Andrew E. Jones
                                       ----------------------------------
                                       Name: Andrew E. Jones
                                       Title: General Partner

<Page>

          [SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT - CONTINUED]

                                   NAS PARTNERS I L.L.C.

                                   By: /s/ Randall A. Hack
                                       ----------------------------------
                                       Name: Randall A. Hack
                                       Title: Member

                                   NASSAU CAPITAL PARTNERS IV L.P.

                                   By:   Nassau Capital LLC,
                                         its General Partner

                                   By: /s/ Randall A. Hack
                                       ----------------------------------
                                       Name: Randall A. Hack
                                       Title: Member

<Page>

          [SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT - CONTINUED]

                                   SMALLCAP WORLD FUND, INC.

                                   By: /s/ Vincent P. Costi
                                       ----------------------------------
                                       Name: Vincent P. Costi
                                       Title: Vice President

<Page>

          [SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT - CONTINUED]

                                   /s/ David Schaeffer
                                   ----------------------------------
                                   David Schaeffer

<Page>

          [SIGNATURE PAGE TO REGISTRATION RIGHTS AGREEMENT - CONTINUED]

                                   2M TECHNOLOGY VENTURES, L.P.

                                   By:   2M Technology Group LLC,
                                         its General Partner

                                   By: /s/ A. Scott Letier
                                       ----------------------------------
                                       Name: A. Scott Letier
                                       Title: Vice President

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