<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.



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         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

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         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


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                                    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>