<PAGE>   1
                                                                    EXHIBIT 10.9



                            ASSIGNMENT OF SECURITIES

         This Assignment of Securities ( this "Assignment") is entered into as
of the 28th day of July 2000, by and between HMTF Bridge RHY, LLC, a Delaware
limited liability company (the "Assignor"), HM4 Rhythms Qualified Fund, LLC, a
Delaware limited liability company, HM4 Rhythms Private Fund, LLC, a Delaware
limited liability company, HM PG-IV Rhythms, LLC, a Delaware limited liability
company, HM 4-SBS Rhythms Coinvestors, LLC, a Delaware limited liability
company, and HM 4-EQ Rhythms 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 6, 2000 (the "Purchase Agreement"), by and
between Rhythms Netconnections, Inc., 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 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.

         3. TITLE TO CONTRACT RIGHTS. Assignor hereby binds itself, its
successors, and its 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



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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 by and construed in
accordance with the laws of the State of New York.

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                                        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 RHY, LLC



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


                                            ASSIGNEES:


                                            HM 4-EQ RHYTHMS COINVESTORS, LLC



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


                                            HM 4-SBS RHYTHMS COINVESTORS, LLC



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



<PAGE>   4

                                            HM PG-IV RHYTHMS, LLC



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


                                            HM4 RHYTHMS QUALIFIED FUND, LLC



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



                                            HM4 RHYTHMS 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
                                                            SERIES E       NUMBER OF    NUMBER OF      NUMBER OF
                                                            PREFERRED       3-YEAR       5-YEAR         7-YEAR
                                                              STOCK        WARRANTS     WARRANTS       WARRANTS
                                        PERCENTAGE            TO BE         TO BE        TO BE          TO BE
             ASSIGNEE                   TRANSFERRED         ACQUIRED       ACQUIRED     ACQUIRED       ACQUIRED
             --------                   -----------         --------       --------     --------       --------

<S>                                      <C>                 <C>           <C>           <C>           <C>
HM4 Rhythms Qualified Fund, LLC          90.994792%          113,743       853,076       853,076       853,076
HM4 Rhythms Private Fund, LLC             0.644644%              806         6,044         6,044         6,044
HM PG-IV Rhythms, LLC                     4.844421%            6,056        45,416        45,416        45,416
HM 4-SBS Rhythms Coinvestors, LLC         2.179044%            2,724        20,429        20,429        20,429
HM 4-EQ Rhythms Coinvestors, LLC          1.337099%            1,671        12,535        12,535        12,535
Total                                     100.0000%          125,000       937,500       937,500       937,500
</TABLE>