<PAGE>

                                                                   Exhibit 10.55

                          FIRST AMENDMENT TO GUARANTY

          THIS FIRST AMENDMENT TO GUARANTY (this "Amendment"), dated as of
December 2, 1999, is made between CAIS Internet, Inc., a Delaware corporation
("Guarantor") and Cisco Systems Capital Corporation , a Nevada corporation
("Lender").

          CAIS, Inc. (the "Borrower")  and Lender are parties to that certain
Agreement dated as of June 30, 1999 (as amended, modified, renewed or extended
from time to time, the "Credit Agreement") and in connection thereto Guarantor
agreed to guarantee the indebtedness and other obligations of the Borrower to
Lender under or in connection with that certain Guaranty dated June 30, 1999
made by Guarantor in favor of Lender (as amended, modified, renewed or extended
from time to time, the "Guaranty").  Guarantor has requested that Lender agree
to certain amendments to the Guaranty.  Lender has agreed to such request,
subject to the terms and conditions hereof.

          Accordingly, the parties hereto agree as follows:

          SECTION 1    Definitions; Interpretation.
                       ----------------------------

          (a)  Terms Defined in the Guaranty. All capitalized terms used in this
               -----------------------------
Amendment (including in the recitals hereof) and not otherwise defined herein
shall have the meanings assigned to them in the Guaranty.

          SECTION 2    Amendments to the Guaranty.
                       ---------------------------

          (a)  Amendments. The Guaranty shall be amended as follows, effective
               ----------
as of the date of satisfaction of the conditions set forth in Section 3 hereof
(the "Effective Date"):

               (i)  Section 9(k) of the Guaranty is hereby amended and restated
in its entirety as follows:

     (k)  On a consolidated basis, Guarantor and its Subsidiaries shall maintain
total revenues of the Guarantor and its Subsidiaries for each quarterly period
set forth below of not less than the correlative amount indicated:

               -----------------------------------------------------
               Quarterly Period Ending         Required Amount
               -----------------------------------------------------
                December 31, 1999                       $  3,508,504
               -----------------------------------------------------
                   March 31, 2000                       $  5,800,000
               -----------------------------------------------------
                    June 30, 2000                       $  8,500,000
               -----------------------------------------------------
               September 30, 2000                       $ 13,278,085
               -----------------------------------------------------
                December 31, 2000                       $ 17,811,138
               -----------------------------------------------------
                   March 31, 2001                       $ 23,815,387
               -----------------------------------------------------
                    June 30, 2001                       $ 28,159,788
               -----------------------------------------------------
               September 30, 2001                       $ 32,520,046
               -----------------------------------------------------
                December 31, 2001                       $ 37,073,989
               -----------------------------------------------------
                   March 31, 2002                       $ 42,500,000
               -----------------------------------------------------

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               -----------------------------------------------------
               Quarterly Period Ending         Required Amount
               -----------------------------------------------------
                    June 30, 2002                       $ 49,300,000
               -----------------------------------------------------
               September 30, 2002                       $ 52,700,000
               -----------------------------------------------------
                December 31, 2002                       $ 55,250,000
               -----------------------------------------------------

               (ii)      Section 9(l) of the Guaranty is hereby amended and
restated in its entirety as follows:

     (l)  On a consolidated basis, Guarantor and its Subsidiaries shall maintain
EBITDA for each quarterly period set forth below of not less than the
correlative ratio indicated (bracketed amounts (()) are negative):

               -----------------------------------------------------
               Quarterly Period Ending         Required Amount
               -----------------------------------------------------
                December 31, 1999                     ($16,056,506)
               -----------------------------------------------------
                   March 31, 2000                     ($16,690,179)
               -----------------------------------------------------
                    June 30, 2000                     ($17,313,272)
               -----------------------------------------------------
               September 30, 2000                     ($16,025,469)
               -----------------------------------------------------
                December 31, 2000                     ($14,569,772)
               -----------------------------------------------------
                   March 31, 2001                     ($ 8,729,733)
               -----------------------------------------------------
                    June 30, 2001                     ($ 5,323,008)
               -----------------------------------------------------
               September 30, 2001                     ($ 1,395,275)
               -----------------------------------------------------
                December 31, 2001                      $ 2,131,229
               -----------------------------------------------------
                   March 31, 2002                      $ 6,800,000
               -----------------------------------------------------
                    June 30, 2002                      $10,000,000
               -----------------------------------------------------
               September 30, 2002                      $10,000,000
               -----------------------------------------------------
               December  31, 2002                      $10,000,000
               -----------------------------------------------------

     "EBITDA" shall mean with respect to any fiscal period of a Person, such
Person's earnings (excluding extraordinary items (determined in accordance with
GAAP, consistently applied)), plus (except to the extent attributable to
                              ----
extraordinary items (determined in accordance with GAAP, consistently applied))
the amount of any interest, taxes, depreciation, amortization deducted in
arriving at such earnings, and, without duplication, plus losses and less gains
                                                     ----
upon dispositions of properties added or deducted in arriving at such earnings.

          (b)  References Within Guaranty. Each reference in the Guaranty to
               --------------------------
"this Guaranty" and the words "hereof," "herein," "hereunder," or words of like
import, shall mean and be a reference to the Guaranty as amended by this
Amendment.

          SECTION 3      Conditions of Effectiveness. Section 2 of this
                         ---------------------------
Amendment shall become effective as of the date on which the Lender has received
from the Guarantor an executed counterpart of this Amendment and the consent of
the Borrower in substantially the form of Exhibit A (the "Borrower Consent"), to
the amendments contemplated by this Amendment.

          SECTION 4      Representations and Warranties. To induce Lender to
                         ------------------------------
enter into this Amendment, Guarantor hereby confirms and restates, as of the
date hereof, the
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representations and warranties made by it in Section 8 of the Guaranty and in
the other Loan Documents. For the purposes of this Section 4, (i) each reference
in Section 8 of the Guaranty to "this Guaranty," and the words "hereof,"
"herein," "hereunder," or words of like import in such Section, shall mean and
be a reference to the Guaranty as amended by this Amendment and (ii) clause (i)
shall take into account any amendments to any disclosures made in writing by
Guarantor and any Guarantor to Lender after the Closing Date and approved by
Lender.

          SECTION 5      Miscellaneous.
                         -------------

          (a)  Guaranty Otherwise Not Affected. Except as expressly amended
               -------------------------------
pursuant hereto, the Guaranty shall remain unchanged and in full force and
effect and is hereby ratified and confirmed in all respects. Lender's execution
and delivery of, or acceptance of, this Amendment and any other documents and
instruments in connection herewith (collectively, the "Amendment Documents")
shall not be deemed to create a course of dealing or otherwise create any
express or implied duty by it to provide any other or further amendments,
consents or waivers in the future.

          (b)  No Reliance. Guarantor hereby acknowledges and confirms to Lender
               -----------
that Guarantor is executing this Amendment and the other Amendment Documents on
the basis of its own investigation and for its own reasons without reliance upon
any agreement, representation, understanding or communication by or on behalf of
any other Person.

          (c)  Costs and Expenses. Guarantor agrees to pay to Lender on demand
               ------------------
the reasonable out-of-pocket costs and expenses of Lender, and the reasonable
fees and disbursements of counsel to Lender, in connection with the negotiation,
preparation, execution and delivery of this Amendment and any other documents to
be delivered in connection herewith.

          (d)  Binding Effect. This Amendment shall be binding upon, inure to
               --------------
the benefit of and be enforceable by Guarantor, Lender and their respective
successors and assigns.

          (e)  Governing Law. This Agreement shall be governed by, and construed
               -------------
in accordance with, the law of the State of New York.

          (f)  Complete Agreement; Amendments. This Amendment, together with the
               ------------------------------
other Amendment Documents and the other Loan Documents, contains the entire and
exclusive agreement of the parties hereto and thereto with reference to the
matters discussed herein and therein. This Amendment supersedes all prior
commitments, drafts, communications, discussions and understandings, oral or
written, with respect thereto. This Amendment may not be modified, amended or
otherwise altered except in accordance with the terms of Section 13 of the
Guaranty and Section 7.1 of the Credit Agreement.

          (g)  Severability. Whenever possible, each provision of this Amendment
               ------------
shall be interpreted in such manner as to be effective and valid under all
applicable laws and regulations. If, however, any provision of this Amendment
shall be prohibited by or invalid under any such law or regulation in any
jurisdiction, it shall, as to such jurisdiction, be deemed modified to conform
to the minimum requirements of such law or regulation, or, if for any reason it
is not deemed so modified, it shall be ineffective and invalid only to the
extent of such
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prohibition or invalidity without affecting the remaining provisions of this
Amendment, or the validity or effectiveness of such provision in any other
jurisdiction.

          (h)  Counterparts. This Amendment may be executed in any number of
               ------------
counterparts and by different parties hereto in separate counterparts, each of
which when so executed shall be deemed to be an original and all of which taken
together shall constitute but one and the same agreement.

          (i)  Interpretation. This Amendment and the other Amendment Documents
               --------------
are the result of negotiations between and have been reviewed by counsel to
Lender, Guarantor and other parties, and are the product of all parties hereto.
Accordingly, this Amendment and the other Amendment Documents shall not be
construed against Lender merely because of Lender's involvement in the
preparation thereof.

          (j)  Loan Documents. This Amendment and the other Amendment Documents
               --------------
shall constitute Loan Documents.

                           [Signature Page Follows]
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          IN WITNESS WHEREOF, the parties hereto have duly executed this
Amendment, as of the date first above written.

                              CAIS Internet, Inc.


                              By   _______________________________________
                                   Title:

                              Cisco Systems Capital Corporation

                              By   _______________________________________
                                   Title:
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                                   EXHIBIT A
                                   ---------

                               BORROWER CONSENT

                               December 2, 1999

Cisco Systems Capital Corporation
Worldwide Financial Services
Mailstop SJC2-3rd Floor
170 West Tasman Drive
San Jose, CA  95134-1706

          Re:  CAIS Internet, Inc.
               -------------------

Gentlemen:

          Reference is made to that certain Agreement dated as of June 30, 1999
(as amended, modified, renewed or extended from time to time, the "Credit
Agreement") by and between CAIS, Inc. (the "Borrower") and Cisco Systems Capital
Corporation (the "Lender") and in connection therewith, that certain Guaranty
dated June 30, 1999 made by CAIS Internet, Inc. (the "Guarantor") in favor of
Lender (as amended, modified, renewed or extended from time to time, the
"Guaranty").

          The undersigned acknowledges receipt of a copy of the First Amendment
to Guaranty dated December 2, 1999 (the "Amendment") being entered into
concurrently herewith by and between CAIS Internet, Inc. and the Lender.

          The undersigned, in its capacity as Borrower in the Credit Agreement,
hereby acknowledges that its consent to the foregoing Amendment is not required,
but the undersigned nevertheless does hereby consent to the foregoing Amendment
and to the documents and agreements referred to therein and to all future
modifications and amendments thereto and any termination thereof, and to any and
all other present and future documents and agreements between or among the
foregoing parties.  Nothing herein shall in any way limit any of the terms or
provisions of any of the Loan Documents, all of which are hereby ratified and
affirmed in all respects.

                                    Sincerely yours,

                                    CAIS, Inc.

                                    By: _______________________________
                                    Title: ____________________________