Exhibit 4.2


COGENT
COMMUNICATIONS GROUP, INC. 

1.00% CONVERTIBLE SENIOR NOTES DUE 2027


THIS NOTE IS
ISSUED WITH ORIGINAL ISSUE DISCOUNT FOR PURPOSES OF SECTION 1271 ET SEQ. OF THE
INTERNAL REVENUE CODE OF 1986, AS AMENDED, AND THE RULES AND REGULATIONS THEREUNDER.
FOR EACH $1,000 PRINCIPAL AMOUNT OF THIS NOTE, (1) THE ISSUE PRICE IS
$977.50; (2) THE AMOUNT OF THE ORIGINAL ISSUE DISCOUNT IS $22.50;
(3) THE ISSUE DATE IS JUNE 11, 2007; AND (4) THE YIELD TO MATURITY IS
[LATHAM – PLEASE PROVIDE YIELD TO MATURITY]% (COMPOUNDED SEMI-ANNUALLY).


THIS SECURITY HAS
NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
‘‘SECURITIES ACT’’), OR THE SECURITIES LAWS OF ANY STATE OR OTHER JURISDICTION.
NEITHER THIS SECURITY NOR ANY INTEREST OR PARTICIPATION HEREIN MAY BE
REOFFERED, SOLD, ASSIGNED, TRANSFERRED, PLEDGED, ENCUMBERED OR OTHERWISE
DISPOSED OF IN THE ABSENCE OF SUCH REGISTRATION OR UNLESS SUCH TRANSACTION IS
EXEMPT FROM, OR NOT SUBJECT TO, SUCH REGISTRATION. THE HOLDER OF THIS SECURITY,
BY ITS ACCEPTANCE HEREOF, (1) REPRESENTS THAT IT IS A ‘‘QUALIFIED INSTITUTIONAL
BUYER’’ (AS DEFINED IN RULE 144A UNDER THE SECURITIES ACT (‘‘RULE 144A’’)); (2)
AGREES ON ITS OWN BEHALF AND ON BEHALF OF ANY INVESTOR ACCOUNT FOR WHICH IT HAS
PURCHASED SECURITIES, TO OFFER, SELL OR OTHERWISE TRANSFER SUCH SECURITY OR ANY
OF THE COMMON STOCK ISSUABLE UPON CONVERSION OF SUCH SECURITY, PRIOR TO THE
EXPIRATION OF THE HOLDING PERIOD APPLICABLE TO SALES OF THIS SECURITY UNDER
RULE 144(k) UNDER THE SECURITIES ACT (OR ANY SUCCESSOR PROVISION), ONLY (A) TO
THE ISSUER, (B) PURSUANT TO A REGISTRATION STATEMENT THAT HAS BEEN DECLARED
EFFECTIVE UNDER THE SECURITIES ACT (AND WHICH CONTINUES TO BE EFFECTIVE AT THE
TIME OF SUCH TRANSFER), (C) FOR SO LONG AS THE SECURITIES ARE ELIGIBLE FOR
RESALE PURSUANT TO RULE 144A, IN COMPLIANCE WITH RULE 144A TO A PERSON IT
REASONABLY BELIEVES IS A QUALIFIED INSTITUTIONAL BUYER THAT PURCHASES FOR ITS
OWN ACCOUNT OR FOR THE ACCOUNT OF A QUALIFIED INSTITUTIONAL BUYER TO WHOM
NOTICE IS GIVEN THAT THE TRANSFER IS BEING MADE IN RELIANCE ON RULE 144A OR (D)
PURSUANT TO ANOTHER AVAILABLE EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF
THE SECURITIES ACT, SUBJECT TO THE ISSUER’S AND THE TRUSTEE’S RIGHT PRIOR TO
ANY SUCH OFFER, SALE OR TRANSFER PURSUANT TO CLAUSE (D) TO REQUIRE THE DELIVERY
OF AN OPINION OF COUNSEL, AND IN ANY CASE A CERTIFICATION AND/OR 



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OTHER INFORMATION
SATISFACTORY TO EACH OF THEM; AND (3) AGREES THAT IT WILL DELIVER TO EACH
PERSON TO WHOM THIS SECURITY IS TRANSFERRED A NOTICE SUBSTANTIALLY TO THE
EFFECT OF THIS LEGEND. THIS LEGEND WILL BE REMOVED UPON THE EARLIER OF THE
TRANSFER OF THIS SECURITY PURSUANT TO CLAUSE 2(B) ABOVE OR UPON ANY TRANSFER OF
THIS SECURITY UNDER RULE 144 UNDER THE SECURITIES ACT (OR ANY SUCCESSOR
PROVISION).


UNLESS THIS
CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY
TRUST COMPANY, A NEW YORK CORPORATION (“DTC”), NEW YORK, NEW YORK, TO THE
COMPANY OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY
CERTIFICATE ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER
NAME AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND ANY PAYMENT IS
MADE TO CEDE & CO. OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED
REPRESENTATIVE OF DTC), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER
HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.


TRANSFERS OF THIS
GLOBAL SECURITY SHALL BE LIMITED TO TRANSFERS IN WHOLE, BUT NOT IN PART, TO
NOMINEES OF DTC OR TO A SUCCESSOR THEREOF OR SUCH SUCCESSOR’S NOMINEE AND
TRANSFERS OF PORTIONS OF THIS GLOBAL SECURITY SHALL BE LIMITED TO TRANSFERS
MADE IN ACCORDANCE WITH THE RESTRICTIONS SET FORTH IN THE INDENTURE REFERRED TO
IN THE TERMS OF SECURITIES ATTACHED HERETO.



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No. 1                                                            Principal
Amount $200,000,000, as revised by the Schedule of Increases and Decreases in
Global Security attached hereto.


CUSIP NO.: 19239V
AA2


ISIN: US19239VAA26


1.00% Convertible Senior Notes due 2027


Cogent Communications Group, Inc., a Delaware
corporation, promises to pay to CEDE & CO., or registered assigns, the
principal sum of TWO HUNDRED MILLION Dollars, as revised by the Schedule of
Increases and Decreases in Global Security attached hereto, on June 15, 2027.


	
  Interest Payment Dates:

  	
   

  	
  June 15 and December 15

  
	
  Regular Record
  Dates:

  	
   

  	
  June 1 and December 1

  



 


Additional provisions of this Security are set forth
on the attached “Terms of Securities.”


	
  Dated: June 11, 2007

  	
   

  	
   

  	
   

  
	
   

  	
   

  	
   

  	
   

  
	
   

  	
   

  	
  COGENT COMMUNICATIONS

  GROUP, INC.

  	
   

  
	
   

  	
   

  	
   

  	
   

  
	
   

  	
   

  	
   

  	
   

  
	
   

  	
   

  	
  By:

  	
   

  	
   

  
	
   

  	
   

  	
   

  	
  Name:

  	
   

  
	
   

  	
   

  	
   

  	
  Title:

  	
   

  
	
   

  	
   

  	
   

  	
   

  	
   

  
	
  TRUSTEE’S CERTIFICATE OF

  AUTHENTICATION

  	
   

  	
   

  	
   

  
	
   

  	
   

  	
   

  	
   

  
	
  WELLS FARGO
  BANK, NATIONAL

  ASSOCIATION

  	
   

  	
   

  	
   

  
	
  as Trustee,
  certifies that this is one of the Securities referred to in the Indenture.

  	
   

  	
   

  	
   

  
	
   

  	
   

  	
   

  	
   

  
	
   

  	
   

  	
   

  	
   

  
	
  By:

  	
   

  	
   

  	
   

  	
   

  
	
   

  	
  Authorized
  Signatory

  	
   

  	
   

  	
   

  



 



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TERMS OF SECURITIES


1.00% Convertible Senior Notes due 2027


The Company issued this Security under an Indenture
dated as of June 11, 2007 (as it may be amended or supplemented from time to
time in accordance with the terms thereof, the “Indenture”),
among the Company and the Trustee, to which reference is hereby made for a
description of the rights, limitations of rights, obligations, duties and
immunities thereunder of the Trustee, the Company and the Holders.  Additional Securities may be issued under the
Indenture in an unlimited aggregate principal amount subject to certain
conditions specified in the Indenture.


1.                                       Interest


Cogent Communications Group, Inc., a Delaware
corporation (such corporation, and its successors and assigns under the
Indenture hereinafter referred to, being herein called the “Company”), promises to pay interest on the principal amount
of this Security at the rate of 1.00% per annum until (but excluding) June 15,
2027.


The Company will pay interest semiannually in arrears
on June 15 and December 15 of each year (each, an “Interest
Payment Date”), commencing December 15, 2007, to Holders of record
on the immediately preceding June 1 and December 1.  Interest on the Securities will accrue from
the most recent date to which interest has been paid on the Securities or, if
no interest has been paid, from June 11, 2007. 
Interest will be computed on the basis of a 360-day year of twelve
30-day months.


2.                                       Method
of Payment


By no later than 11:00 a.m. (New York City time) on
the date on which any principal of, interest (including Additional Interest, if
any) or premium, if any, on any Security is due and payable, the Company shall
deposit with the Paying Agent money sufficient to pay such amount.  The Company will pay principal, premium and
interest in money of the United States that at the time of payment is legal
tender for payment of public and private debts. 
Payments in respect of Securities represented by a Global Security
(including principal, interest (including Additional Interest, if any) and
premium, if any) will be made by wire transfer of immediately available funds
to the accounts specified by The Depository Trust Company.  The Company will pay principal of Definitive
Securities at the office or agency designated by the Company for such
purpose.  Interest (including Additional
Interest, if any), on Definitive Securities will be



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payable (i) to Holders
having an aggregate principal amount of $1,000,000 or less, by check mailed to
the Holders of these Securities and (ii) to Holders having an aggregate
principal amount of more than $1,000,000, either by check mailed to each Holder
or, upon application by a Holder to the Registrar not later than the relevant
record date, by wire transfer in immediately available funds to that Holder’s
account within the United States, which application shall remain in effect
until the Holder notifies, in writing, the Registrar to the contrary.


3.                                       Redemption


Subject to certain conditions specified in the
Indenture, the Securities will be redeemable, at the option of the Company, in
whole at any time or in part from time to time, at any time on or after June
20, 2014 and at a price equal to 100% of the principal amount of Securities to
be redeemed, plus accrued and unpaid interest (including Additional Interest,
if any) to but excluding the Redemption Date provided,
however, that if the Redemption Date falls after a Regular Record Date for the
payment of interest and on or prior to the corresponding Interest Payment Date,
the Company shall pay accrued and unpaid interest to but excluding the
Redemption Date to the  Holder of record
at the close of business on such Regular Record Date on the Interest Payment
Date and the Redemption Price for the Securities will be 100% of the principal
amount of the Securities to be redeemed.


4.                                       Purchase
by the Company at the Option of the Holder; Purchase at the Option of the
Holder Upon a Designated Event


(a)                                  Subject
to the terms and conditions of the Indenture, a Holder shall have the option to
require the Company to purchase all or a portion of its Securities held by such
Holder on each of June 15, 2014, June 15, 2017 and June 15, 2022 (each a “Purchase
Date”) at a Purchase Price specified in the Indenture.


(b)                                 If
a Designated Event shall occur at any time, each Holder shall have the right,
at such Holder’s option and subject to the terms and conditions of the
Indenture, to require the Company to purchase all or a portion of its
Securities at a Designated Event Purchase Price specified in the Indenture.


5.                                       Conversion


Subject to the procedures for conversion set forth in
the Indenture, a Holder may convert its Securities on or prior to the close of
business on the Scheduled Trading Day immediately preceding Stated Maturity
only when one or more of the conditions specified in the Indenture are met and
during the related specified period.  On
or after April 15, 2027, a Holder may convert its Securities at any time prior
to the close of business on the Scheduled Trading Day



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immediately preceding the
Stated Maturity regardless of such conditions specified in the Indenture.


The initial Base Conversion Rate is 20.3355 shares of
Common Stock per $1,000 principal amount of Securities, subject to adjustment
in certain events described in the Indenture. 
Upon conversion, the Company will either (i) deliver shares of Common
Stock based on the Applicable Conversion Rate or (ii) pay cash and shares of
Common Stock, if any, as set forth in the Indenture.  The Company shall deliver cash in lieu of any
fractional share of Common Stock.


A Holder may convert a portion of the Securities only
if the principal amount of such portion is $1,000 or a multiple of $1,000. No
payment or adjustment shall be made for dividends on the Common Stock except as
provided in the Indenture.


6.                                       Denominations;
Transfer; Exchange


The Securities are in registered form without coupons
in denominations of principal amount of $1,000 and multiples of $1,000.  A Holder may transfer or exchange Securities
in accordance with the Indenture.  The
Registrar may require a Holder, among other things, to furnish appropriate
endorsements or transfer documents and to pay any taxes and fees required by
law or permitted by the Indenture.  The
Registrar need not register the transfer of or exchange of Securities (i)               so selected for
redemption or, if a portion of any Security is selected for redemption, the
portion thereof selected for redemption or (ii) surrendered for conversion or,
if a portion of any Security is surrendered for conversion, the portion thereof
surrendered for conversion.


7.                                       Persons
Deemed Owners


The registered Holder of this Security may be treated
as the owner of it for all purposes.


8.                                       Unclaimed
Money


If money for the payment of principal, premium, if
any, or interest (including Additional Interest, if any) remains unclaimed for
two years, the Trustee or Paying Agent shall pay the money back to the Company,
subject to applicable abandoned property laws. 
After any such payment, Holders entitled to the money must look only to
the Company and not to the Trustee for payment.


9.                                       Amendment,
Waiver


Subject to certain exceptions, the Indenture contains
provisions permitting an amendment of the Indenture or the Securities with the
written consent of the Holders of at least a majority in principal amount of
the then outstanding



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Securities and the waiver
of any Event of Default (other than with respect to nonpayment or in respect of
a provision that cannot be amended without the written consent of each Holder
affected) or noncompliance with any provision with the written consent of the
Holders of a majority in principal amount of the then outstanding Securities.


In addition, the Indenture permits an amendment of the
Indenture or the Securities without the consent of any Holder under certain
circumstances specified in the Indenture.


10.                                 Defaults
and Remedies


Subject to the following paragraph, if an Event of
Default specified in the Indenture occurs and is continuing, the Trustee or the
Holders of at least 25% in principal amount of the Securities may declare all
the Securities by notice to the Company to be due and payable immediately.  In addition, certain specified Events of
Default will cause the Securities to become immediately due and payable without
further action by the Holders.


As set forth in the Indenture, the sole remedy for an
Event of Default relating to the Company’s failure to comply with the reporting
obligations under Article 5 of the Indenture, and for any failure to comply
with the requirements of Section 314(a)(1) of the TIA, will for the 60 days
after the occurrence of such an Event of Default consist exclusively of the
right to receive Additional Interest on the principal amount of the Securities
at a rate equal to 0.25% per annum.


Holders may not enforce the Indenture or the
Securities except as provided in the Indenture. 
The Trustee may refuse to enforce the Indenture or the Securities unless
it receives indemnity or security satisfactory to it.  Subject to certain limitations, Holders of a
majority in principal amount of the Securities may direct the Trustee in its
exercise of any trust or power.  The
Trustee may withhold from Holders notice of any continuing Default or Event of
Default (except a Default or Event of Default in payment of principal, interest
(including Additional Interest, if any) or premium, if any) if it determines
that withholding notice is in their interest.


11.                                 Trustee
Dealings with the Company


Subject to certain limitations set forth in the
Indenture, the Trustee under the Indenture, in its individual or any other
capacity, may become the owner or pledgee of Securities and may otherwise deal
with and collect obligations owed to it by the Company or its Affiliates and may
otherwise deal with the Company or its Affiliates with the same rights it would
have if it were not Trustee.



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12.                                 No
Recourse Against Others


An incorporator, director, officer, employee,
Affiliate or stockholder of the Company, solely by reason of this status, shall
not have any liability for any obligations of the Company under the Securities,
the Indenture or for any claim based on, in respect of or by reason of such
obligations or their creation.  By
accepting a Security, each Holder waives and releases all such liability.  The waiver and release are part of the
consideration for the issue of the Securities.


13.                                 Authentication


This Security shall not be valid until an authorized
signatory of the Trustee manually authenticates this Security.


14.                                 Abbreviations


Customary abbreviations may be used in the name of a
Holder or an assignee, such as TEN COM (=tenants in common), TEN ENT (=tenants
by the entirety), JT TEN (=joint tenants with rights of survivorship and not as
tenants in common), CUST (=custodian) and U/G/M/A (=Uniform Gift to Minors
Act).


15.                                 CUSIP
Numbers


Pursuant to a recommendation promulgated by the
Committee on Uniform Security Identification Procedures, the Company has caused
CUSIP numbers to be printed on the Securities and has directed the Trustee to
use CUSIP numbers in notices of redemption as a convenience to Holders.  No representation is made as to the accuracy
of such numbers either as printed on the Securities or as contained in any
notice of redemption, and reliance may be placed only on the other
identification numbers placed thereon.


16.                                 Governing
Law


This Security and the Indenture shall be governed
by, and construed in accordance with, the laws of the State of New York.


The Company will furnish to any Holder upon written
request and without charge to the Holder a copy of the Indenture which has in
it the text of this Security.  Requests
may be made to:


Cogent Communications
Group, Inc.


1015 31st St. NW 


Washington, DC  20007


Attention: Robert N.
Beury, Jr., Chief Legal Officer



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ASSIGNMENT FORM


	
  To assign this
  Security, fill in the form below:

  
	
  I or we assign
  and transfer this Security to

  
	
   

  
	
  (Print or type assignee’s name, address and zip code)

  
	
   

  
	
  (Insert assignee’s soc. sec. or tax I.D. No.)

  
	
  and irrevocably
  appoint                   
  agent to transfer this Security on the books of the Company.  The agent may substitute another to act for
  him.

  
	
   

  
	
  Date:

  	
   

  	
  Your
  Signature:

  	
   

  	
   

  
	
   

  
	
  Signature Guarantee:

  	
   

  
	
  (Signature must be guaranteed)

  
	
   

  
	
   

  
	
  Sign exactly as your
  name appears on the other side of this Security.

  
						



 


The signature(s)
should be guaranteed by an eligible guarantor institution (banks, stockbrokers,
savings and loan associations and credit unions) with membership in an approved
signature guarantee medallion program, pursuant to S.E.C. Rule 17Ad-15.


In connection with
any transfer or exchange of any of the Securities evidenced by this certificate
occurring prior to the date that is two years after the later of the date of
original issuance of such Securities and the last date, if any, on which such
Securities were owned by the Company or any Affiliate of the Company, the
undersigned confirms that such Securities are being:


CHECK ONE BOX
BELOW:


	
  o

  	
  1

  	
  acquired for the
  undersigned’s own account, without transfer; or

  
	
   

  	
   

  	
   

  
	
  o

  	
  2

  	
  transferred to the
  Company; or

  
	
   

  	
   

  	
   

  
	
  o

  	
  3

  	
  transferred pursuant to
  an effective registration statement under the Securities Act of 1933, as
  amended (the “Securities Act”); or

  
	
   

  	
   

  	
   

  
	
  o

  	
  4

  	
  transferred pursuant to
  and in compliance with Rule 144A under the Securities Act; or

  
	
   

  	
   

  	
   

  
	
  o

  	
  5

  	
  transferred pursuant to
  another available exemption from the registration requirements of the
  Securities Act.

  



 


Unless one of the boxes
is checked, the Trustee will refuse to register any of the Securities evidenced
by this certificate in the name of any Person other than the


















registered Holder
thereof; provided, however, that
if box (5) is checked, the Trustee or the Company may require, prior to
registering any such transfer of the Securities, in their sole discretion, such
legal opinions, certifications and other information as the Trustee or the
Company may reasonably request to confirm that such transfer is being made
pursuant to an exemption from, or in a transaction not subject to, the
registration requirements of the Securities Act, such as the exemption provided
by Rule 144 under such Act.


 


	
  

  	
   

  
	
   

  	
  Signature:

  



 


Signature Guarantee:


 


	
  

  	
   

  	
   

  
	
  (Signature must
  be guaranteed)

  	
  Signature:

  



 


The signature(s)
should be guaranteed by an eligible guarantor institution (banks, stockbrokers,
savings and loan associations and credit unions) with membership in an approved
signature guarantee medallion program, pursuant to S.E.C. Rule 17Ad-15.


TO BE COMPLETED BY
PURCHASER IF (4) ABOVE IS CHECKED.


The undersigned represents and warrants that it is purchasing
this Security for its own account or an account with respect to which it
exercises sole investment discretion and that it and any such account is a
“qualified institutional buyer” within the meaning of Rule 144A under the
Securities Act of 1933, as amended, and is aware that the sale to it is being
made in reliance on Rule 144A and acknowledges that it has received such
information regarding the Company as the undersigned has requested pursuant to
Rule 144A or has determined not to request such information and that it is
aware that the transferor is relying upon the undersigned’s foregoing
representations in order to claim the exemption from registration provided by
Rule 144A.


 


	
   

  	
   

  
	
  Dated:

  



 



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SCHEDULE OF
INCREASES OR DECREASES IN GLOBAL SECURITY


The following
increases or decreases in this Global Security have been made:


	
  Date

  	
   

  	
  Amount of decrease

  in Principal Amount

  of this Global

  Security

  	
   

  	
  Amount of increase

  in Principal Amount

  of this Global

  Security

  	
   

  	
  Principal Amount of

  this Global Security

  following such

  decrease or increase

  	
   

  	
  Signature of

  authorized signatory

  of Trustee or

  Securities Custodian

  	
   

  
	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  
	
                        

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  
	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  
	
                               

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  	
   

  



 



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