<PAGE>

                                                                   Exhibit 10.29

                                                                  EXECUTION COPY
                                                                  --------------

                                 COMPLETEL LLC

                            FIRST OMNIBUS AMENDMENT
                            -----------------------

          This First Omnibus Amendment (this "Amendment") is made and entered
                                              ---------
into as of March 24, 2000, by and among CompleTel LLC (the "Company") and the
                                                            -------
other Persons listed on the signature pages hereto (the "Parties").
                                                         -------

          WHEREAS, the Parties, as members of the Company, are party to a Third
Amended and Restated Limited Liability Company Agreement of the Company, dated
as of November 23, 1999 (the "LLC Agreement").
                              -------------

          WHEREAS, the Company and some or all of the Parties are party to each
of the following documents: (i) a Second Amended and Restated Equity Purchase
Agreement dated as of November 23, 1999 (the "Purchase Agreement"); (ii) a
                                              ------------------
Second Amended and Restated Securityholders Agreement (the "Securityholders
                                                            ---------------
Agreement"); (iii) a Second Amended and Restated Registration Agreement (the
---------
"Registration Agreement"); and (iv) a Second Amended and Restated Performance
-----------------------
Vesting Agreement (the "Performance Vesting Agreement").
                        -----------------------------

          WHEREAS, the Company has entered into Executive Securities Agreements
or Employee Securities Agreements with certain employees of the Company and its
Subsidiaries (collectively, the "Executive Securities Agreements").
                                 -------------------------------

          WHEREAS, The LLC Agreement, the Purchase Agreement, the
Securityholders Agreement, the Registration Agreement, and the Executive
Securities Agreements are referred to herein collectively as the "Agreements."
                                                                  ----------
Capitalized terms not otherwise defined herein which are used (i) in Section 2
hereof have the meanings given to such terms in the LLC Agreement, (ii) in
Section 3 hereof have the meanings given to such terms in the Securityholders
Agreement, (iii) in Section 4 hereof have the meanings given to such terms in
the Registration Agreement, (iv) in Section 5 hereof have the meanings given to
such terms in the Performance Vesting Agreement, (v) in Section 6 hereof have
the meanings given to such terms in the Executive Securities Agreements, and
(vi) elsewhere in this Amendment have the meanings given to such terms in the
Purchase Agreement.

          WHEREAS, CompleTel Europe N.V. ("CompleTel Europe"), a Subsidiary of
                                           ----------------
the Company, has filed a registration statement on Form F-1 with the Securities
and Exchange Commission covering CompleTel Europe's proposed issuance of its
ordinary shares to the public (the "Proposed IPO").
                                    ------------

          WHEREAS, in connection with the Proposed IPO, the Company and the
Parties desire to amend and supplement certain provisions of the Agreements as
provided herein.
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          NOW, THEREFORE, in consideration of the mutual promises made herein
and other good and valuable consideration, the receipt and sufficiency of which
are hereby acknowledged, the parties hereto, intending to be legally bound,
agree as follows:

          Section 1.     Amendments to Purchase Agreement.  Upon the
                         --------------------------------
consummation of the Proposed IPO, the following provisions of the Purchase
Agreement will be deemed to be amended and supplemented as follows:

          (a) Solely for purposes of Sections 6C (Restrictive Covenants), 6D
(Affirmative Covenants), 6G (Intellectual Property Rights), and 6H (Public
Disclosures) of the Purchase Agreement, the term "Subsidiary" as used therein
shall be deemed not to include CompleTel Europe or any of its Subsidiaries (the
"Excluded Entities").  As a result, the provisions of Sections 6C, 6D, 6G, and
 -----------------
6H will thereafter no longer apply to actions or inactions of the type
enumerated therein with respect to the Excluded Entities, but such Sections will
continue to apply in full force to actions or inactions of the type enumerated
therein with respect to the Company or any of its Subsidiaries other than the
Excluded Entities.

          (b) Solely for purposes of Section 7 (Purchasers' Put Rights) of the
Purchase Agreement, the term "Qualified Public Offering" as used therein will be
deemed to include the Proposed IPO.  As a result, the put rights of the holders
of Purchaser Securities under Section 7 of the Purchase Agreement will terminate
upon the consummation of the Proposed IPO.

          Section 2.     Amendments to LLC Agreement.  Upon the consummation of
                         ---------------------------
the Proposed IPO, the following provisions of the LLC Agreement will be deemed
to be amended and supplemented as follows:

          (a) Solely for purposes of Section 4.1(i) (Mandatory Conversion) of
the LLC Agreement, the term "Qualified Public Offering" as used therein will be
deemed to include the Proposed IPO.  As a result, all outstanding Preferred
Units will be converted in accordance with the provisions of Section 4.1 of the
LLC Agreement contemporaneously with the consummation of the Proposed IPO; it
                                                                           --
being understood that such conversion will only be effected at the time of and
----------------
subject to the closing of the sale of shares pursuant to the Proposed IPO.

          (b) In connection with the conversion of the Preferred Units described
under paragraph (a) above, the Company will be required pursuant to Section
4.1(a)(v)(B) of the LLC Agreement to pay to each converting holder in cash an
amount equal to the accrued but unpaid Preferred Yield with respect to each
Preferred Unit converted by such holder.  The Company may at its option satisfy
such payment obligation by issuing to each converting holder an additional
number of Common Units (the "Additional Common Units"), such that, immediately
                             -----------------------
after the conversion and the issuance of the Additional Common Units to all
converting holders, the Additional Common Units held by each such converting
holder will represent beneficial ownership of a number of the ordinary shares of
CompleTel Europe held indirectly by the Company equal to the quotient of (x) the
amount of Preferred Yield to be paid to such converting holder in the form of
Common Units, divided by (y) the gross offering price per CompleTel Europe
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ordinary share at which such shares are sold to the public in the Proposed IPO.

                                      -2-
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          (c) The first sentence of Section 3.1(j) of the LLC Agreement will be
amended by inserting the following language at the end of such sentence: ";
provided that the Company will not be required to make such a Distribution of
--------
publicly traded securities with respect to any Units that are (i) subject to
performance vesting or forfeiture under the provisions of the Performance
Vesting Agreement or (ii) subject to time vesting under the provisions of the
Executive Securities Agreements, so long as such Units continue to be subject to
any such restrictions."

          Section 3.     Amendments to Securityholders Agreement.  Upon the
                         ---------------------------------------
consummation of the Proposed IPO, the following provisions of the
Securityholders Agreement will be deemed to be amended and supplemented as
follows:

          (a) Solely for purposes of Section 2 (The Board) of the LLC Agreement,
the term "Securityholder" as used therein will be deemed to refer only to MDCP,
DeGeorge Holdings, Meritage, Allen, Holland, Dovey, Dovey Family Partners LLLP,
Dovey LLC, Pearson, Haj Pearson LLC, Pearson LLC #2, Clevenger, Clevenger LLC,
Clevenger Family LLLP, Lacey, and each of their respective Affiliates or
transferees who hold Securityholder Securities.  As a result, all other
Securityholders will cease to be bound by the voting agreement set forth in
Section 2 of the LLC Agreement upon the consummation of the Proposed IPO.

          (b) Solely for purposes of the definition of the term "Management
Equity" set forth in Section 8 (Definitions) of the LLC Agreement, clause (i) of
such definition will be deleted in its entirety and replaced with the following
language: "(i) the Common Units issued to Dovey, Pearson, Clevenger, and Lacey
(and upon the termination of any such Person's employment with the Company and
its Subsidiaries for any reason, any Key Employee of the Company succeeding to
the position of such Person) under their Executive Securities Agreements (but
not including any Un-Performance-Vested Securities), and".  As a result, Common
Units issued to employees of the Company other than Dovey, Pearson, Clevenger,
Lacey, and their respective replacements, if any, will cease to be included in
the definition of "Management Equity" upon the consummation of the Proposed IPO.

          Section 4.     Amendments to Registration Agreement.  Upon the
                         ------------------------------------
consummation of the Proposed IPO, the Registration Agreement will be deemed to
be amended and supplemented by the terms of the First Supplement to Second
Amended and Restated Registration Agreement, which is attached hereto as Exhibit
                                                                         -------
A (the "RA Supplement").  By operation of this Amendment, the RA Supplement will
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be incorporated into and become a part of the Registration Agreement and will
become effective against the parties to the Registration Agreement at the time
and in the manner set forth in Section 7 hereof.  After CompleTel Europe has
executed the signature page to the RA Supplement, such RA Supplement will be
valid, binding, and effective against CompleTel Europe when such RA Supplement
becomes effective as an amendment to the Registration Agreement as set forth in
Section 7 hereof.

          Section 5.     Amendments to Performance Vesting Agreement.  Upon the
                         -------------------------------------------
consummation of the Proposed IPO, the following provisions of the Performance
Vesting Agreement will be deemed to be amended and supplemented as follows:

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<PAGE>

          (a) Solely for purposes of Section 4 (Performance Vesting of Cliff
Management Securities) of the Performance Vesting Agreement, the term "Qualified
Public Offering" as used therein will be deemed to include the Proposed IPO.  As
a result, the vesting of Cliff Management Securities and the forfeiture of
Forfeitable Purchaser Securities described in Section 4 of the Performance
Vesting Agreement to occur upon a Qualified Public Offering will occur upon the
consummation of the Proposed IPO.

          (b) Solely for purposes of Section 3 (Performance Vesting of Slope
Management Securities), any sale or transfer of any of the CompleTel Europe
ordinary shares which are beneficially represented by the MDCP Securities (the
"MDCP Ordinary Shares") will be deemed to be a sale or transfer of the portion
---------------------
of the MDCP Securities which beneficially represent such transferred MDCP
Ordinary Shares, and any consideration received by or distributed to MDCP from
the sale or transfer of such MDCP Ordinary Shares will be deemed to be
consideration received by MDCP from the deemed sale or transfer of the MDCP
Securities which beneficially represent such transferred MDCP Ordinary Shares.
By way of example, if, after the consummation of the Proposed IPO, (i) 50% of
the MDCP Ordinary Shares were sold by the Company or its Subsidiaries to a third
party and the proceeds from such sale were distributed to MDCP, MDCP would for
purposes of Section 3 of the Performance Vesting Agreement be deemed to have
sold 50% of the MDCP Securities for consideration equal to the amount of such
distributed proceeds, or (ii) 50% of the MDCP Ordinary Shares were distributed
to MDCP, and MDCP sold such MDCP Ordinary Shares to a third party, MDCP would
for purposes of Section 3 of the Performance Vesting Agreement be deemed to have
sold 50% of the MDCP Securities for consideration equal to the amount of
consideration received by MDCP upon the sale of such MDCP Ordinary Shares.

          Section 6.     Accelerated Vesting under Executive Securities
                         ----------------------------------------------
Agreements.
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          (a) Upon consummation of the Proposed IPO, (i) each Executive
Securities Agreement to which one of the Parties is a party will be amended and
supplemented as set forth in paragraph (b) below, (ii) with respect to any other
Executive Securities Agreement, the Company accepts, acknowledges, and agrees
that it will be bound to interpret and enforce such Executive Securities
Agreement as if such agreement were amended and supplemented as set forth in
paragraph (b) below.  The Parties hereto accept, acknowledge, and agree that the
provisions of clause (ii) of the preceding sentence (and, by reference,
paragraph (b) below) are intended for the benefit of certain employees of the
Company and its Subsidiares who are party to Executive Securities Agreements but
not Party hereto, that such Persons are third-party beneficiaries of such
provisions, and that such provisions will be enforceable by such Persons as
provided herein.

          (b) Solely for purposes of the vesting provisions of the Executive
Securities Agreements, the term "Qualified Public Offering" as used therein will
be deemed to include the Proposed IPO.  As a result, (i) the performance vesting
of any Replication Securities which is to occur upon the consummation of a
Qualified Public Offering will occur upon the consummation of the Proposed IPO,
and (ii) the acceleration of time vesting of any Executive Securities which is
to occur upon the consummation of a Qualified Public Offering will occur upon
the consummation of the Proposed IPO.

                                      -4-
<PAGE>

          Section 7.     Effectiveness of Amendment.
                         --------------------------

          (a) This Amendment will be valid, binding, and effective against each
Party as to all Agreements when it has been signed by such Party.  Pursuant to
the respective amendment provisions of each of the Agreements, this Amendment
will be valid, binding, and effective against all parties to a particular
Agreement (including the Parties) when it has been signed by Parties
constituting the requisite vote required to amend such Agreement pursuant to the
amendment provisions thereof.

          (b) The Agreements will be deemed to be amended, supplemented, and
modified as set forth in this Amendment only: (i) upon the consummation of the
Proposed IPO, and (ii) if the proceeds (net of underwriting discounts and
              ---
commissions) received by CompleTel Europe in exchange for the ordinary shares
issued in the Proposed IPO equal or exceed $60 million, and (iii) if the price
                                                        ---
per CompleTel Europe ordinary share paid to CompleTel Europe in such Proposed
IPO equals or exceeds the product of (x) 3.0 times (y) the quotient of (A) the
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aggregate capital contributions made on or prior to the date of such Proposed
IPO with respect to all Purchaser Securities then outstanding which are derived
from the Series A Preferred Units, divided by (B) the number of CompleTel Europe
ordinary shares beneficially represented by all Purchaser Securities (on a fully
diluted, as-if-converted basis) outstanding immediately prior to the
consummation of such Proposed IPO which are derived from the Series A Preferred
Units.

          (c) This Amendment will terminate and be of no further force and
effect if the Proposed IPO, meeting the requirements set forth in paragraph (b)
above, has not been consummated on or prior to April 30, 2000 (or such later
termination date as may be agreed to in writing by the Company, MDCP, and
DeGeorge Holdings).

          (d) The provisions of the Agreements will be amended, supplemented, or
modified only as expressly set forth in this Amendment.  After the consummation
of the Proposed IPO, the Agreements will continue in full force and effect as
amended hereby.

          Section 8.     Miscellaneous.
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          8.1  Counterparts.  This Amendment may be executed in two or more
               ------------
counterparts, any one of which need not contain the signatures of more than one
Party hereto, but each of which will be considered an original and all of which
taken together will constitute one and the same Amendment.

          8.2  Descriptive Headings; Exhibit.  The descriptive headings of this
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Amendment are inserted for convenience only and do not constitute a substantive
part of this Amendment.  The Exhibit hereto is an integral part of this
Agreement, and such Exhibit is by this reference incorporated herein and made a
part hereof.

          8.3  Governing Law.  All issues and questions concerning the
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construction, validity, enforcement and interpretation of this Amendment will be
governed by, and construed in accordance with, the laws of the State of
Delaware, without giving effect to any

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choice of law or conflict of law rules or provisions (whether of the State of
Delaware or any other jurisdiction) that would cause the application of the
laws of any jurisdiction other than the State of Delaware.

          8.4  Delivery by Facsimile.  This Amendment, the agreements referred
               ---------------------
to herein, and each other agreement or instrument entered into in connection
herewith or therewith or contemplated hereby or thereby, and any amendments
hereto or thereto, to the extent signed and delivered by means of a facsimile
machine, will be treated in all manner and respects as an original agreement or
instrument and will be considered to have the same binding legal effect as if it
were the original signed version thereof delivered in person.  At the request of
any Party hereto or to any such agreement or instrument, each other Party hereto
or thereto will reexecute original forms thereof and deliver them to all other
Parties. No Party hereto or to any such agreement or instrument will raise the
use of a facsimile machine to deliver a signature or the fact that any signature
or agreement or instrument was transmitted or communicated through the use of a
facsimile machine as a defense to the formation or enforceability of a contract
and each such party forever waives any such defense.

                         *    *     *    *

                                      -6-
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          IN WITNESS WHEREOF, the Parties hereto have executed this Omnibus
Amendment as of the date first written above.

                         COMPANY:
                         --------

                         COMPLETEL, LLC

                         By  ____________________________________________
                              James E. Dovey, its Chairman and CEO


                         PARTIES:
                         --------

                         DeGEORGE TELCOM HOLDINGS LIMITED
                         PARTNERSHIP

                         By DeGeorge Telcom, LLC, its general partner

                         By       /s/ Lawrence F. DeGeorge
                             --------------------------------------------
                               Lawrence F. DeGeorge, its Manager


                         MADISON DEARBORN CAPITAL PARTNERS II, L.P.

                         By Madison Dearborn Partners II, L.P., its general
                            partner

                         By Madison Dearborn Partners, Inc., its general partner

                         By      /s/ Paul Finnegan
                             --------------------------------------------

                         Its             Managing Director
                               ------------------------------------------


                         MERITAGE PRIVATE EQUITY FUND, L.P.

                         By Meritage Investment Partners, LLC, its general
                            partner

                         By: ___________________________________________
                              Managing Member


                         _____________________________________________
                         James C. Allen

                         _____________________________________________
                         Royce J. Holland

                                      -7-
<PAGE>

                         _____________________________________________
                         George T. Laub


                         _____________________________________________
                         Reed E. Hundt


                         DOVEY FAMILY PARTNERS LLLP


                         By  _________________________________________
                              James E. Dovey, its general partner


                         DOVEY COMPANY LLC


                         By  _________________________________________
                              James E. Dovey, its manager



                         _____________________________________________
                         James E. Dovey



                         _____________________________________________
                         William H. Pearson



                         _____________________________________________
                         Richard N. Clevenger



                         _____________________________________________
                         David E. Lacey

                                      -8-
<PAGE>

                         HAJ PEARSON LLC


                         By  _________________________________________
                              William H. Pearson, its manager



                         HAJ LLC


                         By  _________________________________________
                              William H. Pearson, its manager



                         CLEVENGER COMPANY LLC


                         By  _________________________________________
                              Richard N. Clevenger, its manager



                         CLEVENGER FAMILY LLLP


                         By  _________________________________________
                              Richard N. Clevenger, its general partner

                                      -9-
<PAGE>

                         _____________________________________________
                         Emile Karafiol


                         _____________________________________________
                         William S. Kirsch


                         NORTHWESTERN UNIVERSITY


                         By  __________________________________________

                         Its   ________________________________________


                         SILVER CROSS INVESTORS LLC


                         By  __________________________________________

                         Its   ________________________________________

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