Document:

<PAGE>   1
                                                                    EXHIBIT 10.8

                            ASSIGNMENT OF SECURITIES

         This Assignment of Securities ( this "Assignment") is entered into as
of the 21st day of July 2000, by and between HMTF Bridge ICG, LLC, a Delaware
limited liability company (the "Assignor"), and HM4 ICG Qualified Fund, LLC, a
Delaware limited liability company, HM4 ICG Private Fund, LLC, a Delaware
limited liability company, HM PG-IV ICG, LLC, a Delaware limited liability
company, HM 4- SBS ICG Coinvestors, LLC, a Delaware limited liability company,
and HM 4-EQ ICG Coinvestors, LLC, a Delaware limited liability company
(collectively, the "Assignees").

                                    RECITALS

         A. Assignor is a party to that certain Preferred Stock and Warrant
Purchase Agreement, dated February 27, 2000 (the "Purchase Agreement"), by and
between ICG Communications, Inc., a Delaware corporation (the "Company"), and
each of the Purchasers listed on Schedule I thereto. Capitalized terms not
otherwise defined herein shall have the meaning ascribed to such terms in the
Purchase Agreement.

         B. Assignor desires to assign and delegate to Assignees all of
Assignor's rights, titles, and interests in and to the Purchase Agreement.

                                   AGREEMENTS

         NOW, THEREFORE, in consideration of the covenants of Assignees
hereunder and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto, intending to
be legally bound, hereby agree as follows:

         1. ASSIGNMENT. Pursuant to Section 8.12 of the Purchase Agreement,
Assignor hereby sells, assigns, transfers, and conveys to each Assignee and its
respective successors and assigns the percentage of Assignor's rights, titles,
interests, and obligations in, to, and under the Purchase Agreement as set forth
opposite such Assignee's name on Exhibit A (including, without limitation, the
right to amend, terminate, supplement, and extend the Purchase Agreement,
collectively the "Contract Rights").

         2. ASSUMPTION. Each Assignee hereby agrees to assume and perform all
Contract Rights of the Assignor hereby sold, assigned, transferred, and conveyed
to such Assignee and agrees to be bound by the terms of the Purchase Agreement
to which Assignor is a party. Except as expressly set forth in this Assignment,
Assignees do not hereby assume or agree to pay any other liabilities or
obligations of Assignor of any nature whatsoever.

         3. TITLE TO CONTRACT RIGHTS. Assignor hereby binds itself, its
successors, and its assigns to warrant and defend, all and singular, title to
the Contract Rights unto Assignees and their

<PAGE>   2

respective successors and assigns against every person lawfully claiming or to
claim the same or any part thereof. Assignor warrants to each Assignee that it
is conveying good title to the Contract Rights free and clear of all Liens.

         4. POWER OF ATTORNEY. Assignor hereby constitutes and appoints each
Assignee as Assignor's true and lawful attorney, with full power of
substitution, for it and in its name, place, and stead, but on behalf of and for
the benefit of such Assignee, (a) to demand and receive from time to time any
and all Contract Rights and to get receipts and releases for and in respect of
the same or any part thereof and (b) to do generally all and any such acts and
things in relation thereto as such Assignee shall deem advisable.

         5. FURTHER ASSURANCES. Assignor, for itself and its successors and
assigns, hereby covenants and agrees with Assignees that Assignor will do,
execute, acknowledge, and deliver, or will cause to be done, executed,
acknowledged, and delivered, all such further acts, conveyances, transfers,
assignments, powers of attorney, and assurances as may be required to assure,
convey, transfer, confirm, and vest unto Assignees any and all of the Contract
Rights and to aid and assist Assignees in collecting and reducing the same to
possession.

         6. PRIVATE PLACEMENT.

                  (a) Each Assignee understands that the transactions
contemplated by this Assignment are intended to be exempt from registration
under the Securities Act and that there is no existing public or other market
for the Securities.

                  (b) Each Assignee (either alone or together with its advisors)
has sufficient knowledge and experience in financial and business matters so as
to be capable of evaluating the merits and risks of its investment in the
Securities, the Conversion Shares, and the Warrant Shares and is capable of
bearing the economic risks of such investment.

                  (c) Each Assignee is acquiring the Securities, the Conversion
Shares, and the Warrant Shares for its own account (or for accounts over which
it exercises investment authority) for investment and not with a view to the
public resale or distribution thereof in violation of any securities law.

                  (d) Each Assignee understands that the Securities, the
Conversion Shares, and the Warrant Shares have been issued in a transaction
exempt from the registration or qualification requirements of the Securities Act
and applicable state securities laws and that such securities must be held
indefinitely unless a subsequent disposition thereof is registered or qualified
under the Securities Act and such state securities laws or is exempt from such
registration or qualification.

                  (e) Such Assignee (A) has been furnished with or has had full
access to all of the information that it has requested from ICG Communications,
Inc. and that it considers necessary or

                                       2
<PAGE>   3

appropriate to make an informed investment decision with respect to the
Securities, the Conversion Shares, and the Warrant Shares, (B) has had an
opportunity to discuss with management of ICG Communications, Inc. the intended
business and financial affairs of ICG Communications, Inc. and to obtain
information (to the extent ICG Communications, Inc. possessed such information
or could acquire it without unreasonable effort or expense) necessary to verify
any information furnished to it or to which it had access, (C) can bear the
economic risk of (x) an investment in the Securities, the Conversion Shares, and
the Warrant Shares indefinitely and (y) a total loss in respect of such
investment, and (D) has such knowledge and experience in business and financial
matters so as to enable it to understand and evaluate the risks of and form an
investment decision with respect to its investment in the Securities, the
Conversion Shares, and the Warrant Shares and to protect its own interest in
connection with such investment.

                  (f) The foregoing representations with respect to the
Conversion Shares and the Warrant Shares are made only if and to the extent the
offering of the Shares and the Warrants constitutes an offering of the
Conversion Shares and the Warrant Shares.

         7. PERMITTED TRANSFEREE. Each Assignee hereby represents and warrants
as to itself that it is a Permitted Transferee.

         8. GOVERNING LAW. This Assignment shall be governed by and construed in
accordance with the laws of the State of New York.

            [The remainder of this page is left intentionally blank]

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<PAGE>   4

         IN WITNESS WHEREOF, the undersigned have caused this Agreement to be
signed, all as of the date first written above.

                                    ASSIGNOR:

                                    HMTF BRIDGE ICG, LLC

                                    By: /s/ David W. Knickel
                                       -----------------------------------
                                    Name:   David W. Knickel
                                         ---------------------------------
                                    Title:   Vice President
                                          --------------------------------

                                    ASSIGNEES:

                                    HM4 ICG QUALIFIED FUND, LLC

                                    By: /s/ David W. Knickel
                                       -----------------------------------
                                    Name:   David W. Knickel
                                         ---------------------------------
                                    Title:   Vice President
                                          --------------------------------

                                    HM4 ICG PRIVATE FUND, LLC

                                    By: /s/ David W. Knickel
                                       -----------------------------------
                                    Name:   David W. Knickel
                                         ---------------------------------
                                    Title:   Vice President
                                          --------------------------------

<PAGE>   5

                                    HM PG-IV ICG, LLC

                                    By: /s/ David W. Knickel
                                       -----------------------------------
                                    Name:   David W. Knickel
                                         ---------------------------------
                                    Title:   Vice President
                                          --------------------------------

                                    HM 4-SBS ICG COINVESTORS, LLC

                                    By: /s/ David W. Knickel
                                       -----------------------------------
                                    Name:   David W. Knickel
                                         ---------------------------------
                                    Title:   Vice President
                                          --------------------------------

                                    HM 4-EQ ICG COINVESTORS, LLC

                                    By: /s/ David W. Knickel
                                       -----------------------------------
                                    Name:   David W. Knickel
                                         ---------------------------------
                                    Title:   Vice President
                                          --------------------------------

<PAGE>   6

                                    EXHIBIT A

                            ASSIGNMENT OF SECURITIES

<TABLE>
<CAPTION>
                                                   SHARES OF ICG
                                                    8% SERIES A
                                                    CONVERTIBLE        NUMBER OF
                                  PERCENTAGE      PREFERRED STOCK       WARRANTS
       ASSIGNEE                   TRANSFERRED      TO BE ACQUIRED    TO BE ACQUIRED
-----------------------------     -----------     ---------------    --------------
<S>                                <C>                 <C>             <C>
HM4 ICG Qualified Fund, LLC        90.994792%          10,464          1,395,254
HM4 ICG Private Fund, LLC           0.644644%              74              9,885
HM PG-IV ICG, LLC                   4.844421%             557             74,281
HM 4-SBS ICG Coinvestors, LLC       2.179044%             251             33,412
HM 4-EQ ICG Coinvestors, LLC        1.337099%             154             20,502
Total                             100.0000%            11,500          1,533,334
</TABLE><PAGE>   1
                                                                   EXHIBIT 10.10

                            ASSIGNMENT OF SECURITIES

         This Assignment of Securities ( this "Assignment") is entered into as
of the 27th day of June 2000, by and between HMTF Bridge Viatel, LLC, a Delaware
limited liability company (the "Assignor"), HMEU Viatel I-EQ Coinvestors, LLC, a
Delaware limited liability company, HMEU Viatel I-SBS Coinvestors, LLC, a
Delaware limited liability company, HM Viatel PG Europe, LLC, a Delaware limited
liability company, HMEU Viatel Qualified Fund, LLC, a Delaware limited liability
company, and HMEU Viatel Private Fund, LLC, a Delaware limited liability company
(collectively, the "Assignees").

                                    RECITALS

         A. Assignor is a party to that certain Securities Purchase Agreement,
dated February 1, 2000 (the "Purchase Agreement") by and between Viatel, Inc., a
Delaware corporation (the "Company"), and each of the security holders listed on
Schedule I thereto. Capitalized terms not otherwise defined herein shall have
the meaning ascribed to such terms in the Purchase Agreement.

         B. Assignor desires to assign and delegate to Assignees all of
Assignor's rights, titles, and interests in and to the Purchase Agreement.

                                   AGREEMENTS

         NOW, THEREFORE, in consideration of the covenants of Assignees
hereunder and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto, intending to
be legally bound, hereby agree as follows:

         1. ASSIGNMENT. Pursuant to Section 8.12 of the Purchase Agreement,
Assignor hereby sells, assigns, transfers, and conveys to each Assignee and its
respective successors and assigns the percentage of Assignor's rights, titles,
interests, and obligations in, to, and under the Purchase Agreement as set forth
opposite such Assignee's name on Exhibit A (including, without limitation, the
right to amend, terminate, supplement, and extend the Purchase Agreement,
collectively the "Contract Rights").

         2. ASSUMPTION. Each Assignee hereby agrees to assume and perform timely
all Contract Rights of the Assignor hereby sold, assigned, transferred, and
conveyed to such Assignee and agrees to be bound by the terms of the Purchase
Agreement and the other Equity Documents to which Assignor was to become a
party. Except as expressly set forth in this Assignment, Assignees do not hereby
assume or agree to pay any other liabilities or obligations of Assignor of any
nature whatsoever.

<PAGE>   2

         3. TITLE TO CONTRACT RIGHTS. Assignor hereby binds itself, its
successors, and assigns to warrant and defend forever, all and singular, title
to the Contract Rights unto Assignees and their respective successors and
assigns against every person lawfully claiming or to claim the same or any part
thereof. Assignor warrants to each Assignee that it is conveying good title to
the Contract Rights free and clear of all Liens.

         4. POWER OF ATTORNEY. Assignor hereby constitutes and appoints each
Assignee as Assignor's true and lawful attorney, with full power of
substitution, for it and in its name, place, and stead, but on behalf of and for
the benefit of such Assignee, (a) to demand and receive from time to time any
and all Contract Rights and to get receipts and releases for and in respect of
the same or any part thereof, and (b) to do generally all and any such acts and
things in relation thereto as such Assignee shall deem advisable.

         5. FURTHER ASSURANCES. Assignor, for itself and its successors and
assigns, hereby covenants and agrees with Assignees that Assignor will do,
execute, acknowledge, and deliver, or will cause to be done, executed,
acknowledged, and delivered, all such further acts, conveyances, transfers,
assignments, powers of attorney, and assurances as may be required to assure,
convey, transfer, confirm, and vest unto Assignees any and all of the Contract
Rights and to aid and assist Assignees in collecting and reducing the same to
possession.

         6. GOVERNING LAW. This Assignment shall be governed and construed in
accordance with the laws of the State of New York.

            [The remainder of this page is left intentionally blank]

                                        2

<PAGE>   3

         IN WITNESS WHEREOF, the undersigned have caused this Agreement to be
signed, all as of the date first written above.

                                    ASSIGNOR:

                                    HMTF BRIDGE VIATEL, LLC

                                    By: /s/ David W. Knickel
                                       ----------------------------------------
                                    Name:   David W. Knickel
                                         --------------------------------------
                                    Title:  Vice President
                                          -------------------------------------

                                    ASSIGNEES:

                                    HMEU VIATEL I-EQ COINVESTORS, LLC

                                    By: /s/ David W. Knickel
                                       ----------------------------------------
                                    Name:   David W. Knickel
                                         --------------------------------------
                                    Title:  Vice President
                                          -------------------------------------

                                    HMEU VIATEL I-SBS COINVESTORS, LLC

                                    By: /s/ David W. Knickel
                                       ----------------------------------------
                                    Name:   David W. Knickel
                                         --------------------------------------
                                    Title:  Vice President
                                          -------------------------------------

                                    HM VIATEL PG EUROPE, LLC

                                    By: /s/ David W. Knickel
                                       ----------------------------------------
                                    Name:   David W. Knickel
                                         --------------------------------------
                                    Title:  Vice President
                                          -------------------------------------

                  [SIGNATURE PAGE TO ASSIGNMENT OF SECURITIES]

                                       S-1

<PAGE>   4

                                    HMEU VIATEL QUALIFIED FUND, LLC

                                    By: /s/ David W. Knickel
                                       ----------------------------------------
                                    Name:   David W. Knickel
                                         --------------------------------------
                                    Title:  Vice President
                                          -------------------------------------

                                    HMEU VIATEL PRIVATE FUND, LLC

                                    By: /s/ David W. Knickel
                                       ----------------------------------------
                                    Name:   David W. Knickel
                                         --------------------------------------
                                    Title:  Vice President
                                          -------------------------------------

<PAGE>   5

                                    EXHIBIT A

                            ASSIGNMENT OF SECURITIES

<TABLE>
<CAPTION>

                                                         SHARES OF VIATEL
                                                            SERIES B-1
                                         PERCENTAGE      PREFERRED STOCK    A-1 WARRANTS       B-1 WARRANTS
                     ASSIGNEE            TRANSFERRED      TO BE ACQUIRED   TO BE ACQUIRED     TO BE ACQUIRED
                     --------            -----------      --------------   --------------     --------------

<S>                                      <C>              <C>              <C>                <C>
HMEU Viatel I-EQ Coinvestors, LLC         1.141922%            928              2,150              2,150

HMEU Viatel I-SBS Coinvestors, LLC        2.303208%           1,871             4,336              4,336

HM Viatel PG Europe, LLC                  6.569706%           5,338            12,369             12,369

HMEU Viatel Qualified Fund, LLC          88.921894%           72,249           167,421            167,421

HMEU Viatel Private Fund, LLC            1.0632780%            864              2,002              2,002

Total                                     100.0000%           81,250           188,278            188,278
</TABLE>

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