<PAGE>
                                                                   EXHIBIT 10.20

                                                     -----------------------
                                                      DATE: APRIL 30, 2003
                                                     -----------------------
Return To:

Emmet, Marvin & Martin, LLP
120 Broadway, 32nd Floor
New York, New York 10271
Attn:  Irving C. Apar





                                                     -----------------------


          SECOND ASSIGNMENT OF LEASES AND RENTS AND SECURITY DEPOSITS


         THIS SECOND ASSIGNMENT OF LEASES AND RENTS AND SECURITY DEPOSITS (this
"Assignment") is made as of April 30, 2003, by NAP OF THE AMERICAS, INC., a
Florida corporation ("Assignor"), whose address is 2601 South Bayshore Drive,
Miami, FL 33133, in favor of THE BANK OF NEW YORK TRUST COMPANY OF FLORIDA, N.A.
("Assignee"), whose address is 10161 Centurion Parkway, Jacksonville, FL 32256.



                              W I T N E S S E T H:

         WHEREAS, Terremark Worldwide, Inc., a Delaware corporation
("Terremark"), which owns all of the outstanding capital stock of Assignor, has
issued and sold 10% Subordinated Secured Convertible Debentures due 2006 (the
"Debentures") and the holders from time to time of the Debentures have appointed
Assignee to act as collateral agent on their behalf.

         WHEREAS, the Debentures are secured by, among other things, that
certain Second Mortgage and Security Agreement, Assignment of Leases and Rents
and Fixture Filing, dated of even date herewith, given by Assignor to Assignee
(the "Second Mortgage"), to be recorded in the Public Records of Miami-Dade
County, Florida prior to the recordation of this Assignment, which Mortgage
encumbers, inter alia, the Leased Premises; all capitalized terms used but not
otherwise defined herein shall have the meanings provided therefore in the
Mortgage.


===============================================================================
NOTWITHSTANDING ANY PROVISIONS CONTAINED HEREIN TO THE CONTRARY, THIS
ASSIGNMENT AND THE LIENS CREATED HEREBY ARE SUBJECT TO AND SUBORDINATE TO THE
LIENS OF THE SENIOR MORTGAGE AND THE OTHER SENIOR LOAN DOCUMENTS (AS SUCH TERMS
ARE DEFINED IN THE FOLLOWING DESCRIBED SUBORDINATION AGREEMENT) PURSUANT TO THAT
CERTAIN SUBORDINATION AGREEMENT BETWEEN ASSIGNEE, ASSIGNOR, OCEAN BANK AND
TERREMARK DATED APRIL 30, 2003, TO BE RECORDED IN THE PUBLIC RECORDS OF
MIAMI-DADE COUNTY, FLORIDA SIMULTANEOUSLY WITH THE RECORDATION OF THIS
ASSIGNMENT WHICH SUBORDINATION AGREEMENT IS INCORPORATED HEREIN BY REFERENCE AND
MADE A PART HEREOF.



<PAGE>


         WHEREAS, the Leased Premises is a portion of that certain real property
situated in the County of Miami-Dade, State of Florida, as is more particularly
described on Exhibit A attached hereto and incorporated herein by this
reference; and

         WHEREAS, Assignor is desirous of further securing to Assignee the
performance of the terms, covenants and agreements hereof and of the other
Subordinated Loan Documents.

         NOW, THEREFORE, in consideration of the purchase of the Debentures and
for other good and valuable consideration, the receipt and sufficiency of which
are hereby acknowledged, Assignor does hereby irrevocably, absolutely and
unconditionally transfer, sell, assign, pledge, bargain, set over and convey to
Assignee, its successors and assigns, all of the right, title and interest of
Assignor, either now existing or hereafter acquired, in and to any and all
Leases and Rents.

         TO HAVE AND TO HOLD the same unto Assignee, its successors and assigns.
IT IS AGREED that this Assignment is made upon the following terms, covenants
and conditions:

         1. This instrument is a present, complete, effective, irrevocable,
absolute and unconditional assignment of the Rents and of the Leases and a
present, absolute, unconditional and executed grant of the powers herein granted
to Assignee, and not an assignment for security; and the existence or exercise
of Assignor's revocable license to collect Rent shall not operate to subordinate
this assignment to any subsequent assignment, and such assignment shall be fully
operative without any further action on the part of any party, and Assignee
shall be entitled upon the occurrence and during the continuance of an Event of
Default to all Rents, whether or not Assignee takes possession of the Mortgaged
Property or any part thereof. Assignor is hereby permitted, at the sufferance of
Assignee and at its discretion, and is hereby granted a revocable license by
Assignee, to collect the Rents and to take all actions with respect to all
Leases, present and future, subject to the terms of the Second Mortgage, this
Assignment and the other Subordinated Loan Documents, unless and until there
shall have occurred and be continuing an Event of Default. Upon the occurrence
and during the Continuance of an Event of Default, the aforementioned license
granted to Assignor automatically shall terminate without notice to Assignor,
and Assignee may thereafter, without taking possession of the Mortgaged
Property, take possession of the Leases and collect the Rents. Further, from and
after such termination, Assignor shall be the agent of Assignee in collection of
the Rents, and any Rents so collected by Assignor shall be held in trust by
Assignor for the sole and exclusive benefit of Assignee and Assignor shall,
within one (1) business day after receipt of any Rents, pay the same to Assignee
to be applied by Assignee as hereinafter set forth. Furthermore, upon the
occurrence and during the Continuance of an Event of Default and termination of
the aforementioned license, Assignee shall have the right and authority, without
any notice whatsoever to Assignor and without regard to the adequacy of the
security therefore, to: (a) manage and operate the Mortgaged Property, with full
power to employ agents to manage the same; (b) demand, collect, receive and sue
for the Rents, including those past due and unpaid; and (c) do all acts relating
to such management of the Mortgaged Property, including, but not limited to,
negotiation of new Leases, making adjustments of existing Leases, contracting



                                      -2-
<PAGE>

and paying for repairs and replacements to the Mortgaged Property or used in any
way in the operation, use and occupancy of the Mortgaged Property as in the sole
subjective judgment and discretion of Assignee may be necessary to maintain the
same in a tenantable condition, purchasing and paying for such additional
furniture and equipment as in the sole subjective judgment of Assignee may be
necessary to maintain a proper rental income from the Mortgaged Property,
employing necessary managers and other employees, purchasing fuel, providing
utilities and paying for all other expenses incurred in the operation of the
Mortgaged Property, maintaining adequate insurance coverage over hazards
customarily insured against and paying the premiums therefore. Assignee may
apply the Rents received by Assignee from the Mortgaged Property, after
deducting the costs of collection thereof, including, without limitation,
attorneys' fees and a management fee for any management agent so employed,
against amounts expended for repairs, upkeep, maintenance, service, fuel,
utilities, taxes, assessments, insurance premiums and such other expenses as
Assignee incurs in connection with the operation of the Mortgaged Property and
against interest, principal, required escrow deposits and other sums which have
or which may become due, from time to time, under the terms of the Subordinated
Loan Documents, in such order or priority as to any of the items so mentioned as
Assignee, in its sole subjective discretion, may determine. The exercise by
Assignee of the rights granted Assignee in this paragraph, and the collection of
the Rents and the application thereof as herein provided, shall not be
considered a waiver by Assignee of any default under the Subordinated Loan
Documents or prevent foreclosure of any liens on the Mortgaged Property nor
shall such exercise make Assignee liable under any of the Leases. Assignee
hereby expressly reserving all of its rights and privileges under the Mortgage
and the other Loan Documents as fully as though this Assignment had not been
entered into.

         2. Assignor agrees to deliver to Assignee, within thirty (30) days
after Assignee's request, a true and complete copy of every Lease and, within
ten (10) days after Assignee's request, a complete list of the Leases, certified
pursuant to an officer's certificate stating the demised premises, the names of
the Lessees, the Rents payable under the Leases, the date to which such Rents
have been paid, the terms of the Leases, the dates of occupancy, the dates of
expiration, any Rent concessions, work obligations or other inducements granted
to the Lessees, and any renewal options.

         3. Without limiting the rights granted hereinabove, upon the occurrence
and during the continuance of an Event of Default, Assignee may, but shall not
be obligated to, without prior notice to or demand on Assignor and without
releasing Assignor from any obligation hereof, make or perform the same in such
manner and to such extent as Assignee may deem necessary to protect the security
hereof, including specifically, without limitation, entering upon the Mortgaged
Property, and collecting, retaining and applying the Rents toward payment of the
Obligations in such priority and proportions as Assignee in its discretion shall
deem proper, disposing by the usual summary proceedings any lessee defaulting in
making any payment due under any Lease or sublease to Assignee or defaulting in
the performance of any of its other obligations under its Lease or sublease,
letting the Mortgaged Property, the Improvements or any portion thereof,
applying the Rents on account of the Obligations, and performing such other acts
as Assignee is entitled to perform hereunder appearing in and defending any
action or proceeding purporting to affect the security hereof or the rights or
powers of Assignee, performing or discharging any obligation, covenant or
agreement of Assignor under any of the Leases, and performing such other acts as



                                      -3-
<PAGE>

Assignee is entitled to perform hereunder, and, in exercising any of such
powers, paying all necessary fees, costs and expenses, employing counsel and
incurring and paying reasonable attorneys' fees and expenses. Any sum advanced
or paid by Assignee for any such purpose, including, without limitation,
reasonable attorneys' fees and expenses, together with interest thereon at the
Default Rate from the date paid or advanced by Assignee until repaid by
Assignor, shall immediately be due and payable to Assignee by Assignor on demand
and shall be secured by the Mortgage and by all of the other Loan Documents. The
execution of this Assignment constitutes and evidences the irrevocable consent
of Assignor to Assignee's entry upon and taking of possession of the Mortgaged
Property or any portion thereof pursuant to the provisions of this Section 3.

         4. In addition to the rights which Assignee may have herein, upon the
occurrence and during the continuance of any Event of Default, Assignee, at its
option, may require Assignor to pay monthly in advance to Assignee, or any
receiver appointed to collect the Rents, the fair and reasonable rental value
for the use and occupation of such part of the Mortgaged Property as may be in
the possession of Assignor and may require Assignor to vacate and surrender
possession of the Mortgaged Property to Assignee or to such receiver and, in
default thereof, Assignor may be evicted by summary proceedings or otherwise.

         5. This Assignment shall not operate to place responsibility for the
control, care, management or repair of the Mortgaged Property upon Assignee, nor
for the performance of any of the terms and conditions of any of the Leases, nor
shall it operate to make Assignee responsible or liable for any waste committed
on the Mortgaged Property by the tenants or any other party or for any dangerous
or defective condition of the Mortgaged Property or for any negligence in the
management, upkeep, repair or control of the Mortgaged Property. Assignee shall
not be liable for any loss sustained by Assignor resulting from Assignee's
failure to let the Mortgaged Property or from any other act or omission of
Assignee in the management, upkeep, repair or control of the Mortgaged Property.
Assignor shall and does hereby indemnify and hold Assignee harmless from and
against any and all liability, loss, claim, demand or damage which may or might
be incurred by reason of this Assignment, including, without limitation, claims
or demands for security deposits from tenants of space in the Improvements
deposited with Assignor, and from and against any and all claims and demands
whatsoever which may be asserted against Assignee by reason of any alleged
obligations or undertakings on its part to perform or discharge any of the
terms, covenants or agreements contained in any of the Leases. Should Assignee
incur any liability by reason of this Assignment or in defense of any claim or
demand for loss or damage as provided above, the amount thereof at the Default
Rate from the date paid or incurred by Assignee until repaid by Assignor shall
be immediately due and payable to Assignee by Assignor upon demand and shall be
secured by the Mortgage and by all of the other Loan Documents. It is expressly
acknowledged and agreed by Assignor that the indemnity contained in this
Agreement protects Assignee from the consequences of Assignee's acts or
omissions, including, without limitation, the negligent acts or omissions of
Assignee, to the extent provided by law; provided, however, that nothing
contained herein shall be deemed to require Assignor to indemnify Assignee from
Assignee's gross negligence or willful misconduct.

         6. This Assignment shall not be construed as making Assignee a
mortgagee-in-possession.

         7. Assignee is obligated to account to Assignor only for such Rents as
are actually collected or received by Assignee.

         8. Assignor hereby further presently and absolutely assigns to Assignee
subject to the terms and provisions of this Assignment: (a) any award or other
payment which Assignor may hereafter become entitled to receive with respect to
any of the Leases as a result of or pursuant to any bankruptcy, insolvency or



                                      -4-
<PAGE>

reorganization or similar proceedings involving the tenants under such Leases;
and (b) any and all payments made by or on behalf of any tenant of any part of
the Mortgaged Property in lieu of Rents. Assignor hereby irrevocably appoints
Assignee as its attorney-in-fact to, upon the occurrence and during the
continuance of an Event of Default, appear in any such proceeding and to collect
any such award or payment, which power of attorney is coupled with an interest
by virtue of this Assignment and is irrevocable so long as any sums are
outstanding under the Loan.

         9. Assignor represents, warrants and covenants to and for the benefit
of Assignee: (a) that Assignor now is (or with respect to any Leases not yet in
existence, will be immediately upon the execution thereof) the absolute owner of
the landlord's interest in the Leases, with full right and title to assign the
same and the Rents due or to become due thereunder; (b) that, other than this
Assignment and the Senior Assignment, there are no outstanding assignments of
the Leases or Rents; (c) that no Rents have been discounted, released, waived,
compromised or otherwise discharged except for prepayment of rent of not more
than one (1) month prior to the accrual thereof; (d) that there are not material
defaults now existing under any of the Leases by the landlord or tenant, and
there exists no state of facts which, with the giving of notice or lapse of time
or both, would constitute a default under any of the Leases by the landlord or
tenant, except as disclosed in writing to Assignee; (e) that Assignor has and
shall duly and punctually observe and perform all covenants, conditions and
agreements in the Leases on the part of the landlord to be observed and
performed thereunder and (f) the Leases are in full force and effect and are the
valid and binding obligations of Assignor, and, to the knowledge of Assignor,
are the valid and binding obligations of the tenants thereto.

         10. Assignor covenants and agrees that Assignor shall not, without the
prior written consent of Assignee: (a) accept any payment of Rent or
installments of Rent for more than one month in advance; (b) enter into any
Lease not in conformity with the provisions of the Mortgage; (c) except as may
be expressly permitted by the provisions of the Mortgage, cancel or terminate
any Lease or amend or modify any Lease; (d) take or omit to take any action or
exercise any right or option which would permit the tenant under any Lease to
cancel or terminate any Lease; (e) discount, release, waive, compromise or
otherwise discharge any Rents payable or other obligations under the Leases; (f)
further pledge, transfer, mortgage or otherwise encumber or assign the Leases or
future payments of Rents or incur any material indebtedness, liability or other
obligation to any tenant, lessee or licensee under the Leases; or (g) permit any
Lease to become subordinate to any lien other than the lien of the Mortgage.

         11. Assignor covenants and agrees that Assignor shall, at its sole cost
and expense, appear in and defend any action or proceeding arising under,
growing out of, or in any manner connected with the Leases or the obligations,
duties or liabilities of the landlord or tenant thereunder, and shall pay on
demand all fees, costs and expenses, including, without limitation, reasonable
attorneys' fees and expenses, which Assignee may incur in connection with
Assignee's appearance, voluntary or otherwise, in any such action or proceeding,
together with interest thereon at the Default Rate from the date incurred by
Assignee until repaid by Assignor.

         12. At any time, Assignee may, at its option, notify any tenants or
other parties of the existence of this Assignment. Assignor does hereby
specifically authorize, instruct and direct each and every present and future


                                      -5-
<PAGE>

tenant, lessee and licensee of the whole or any part of the Mortgaged Property
to pay all unpaid and future Rents to Assignee upon receipt of demand from
Assignee so to pay the same upon the occurrence and during the continuance of an
Event of Default and Assignor hereby agrees that each such present and future
tenant, lessee and licensee may rely upon such written demand from Assignee so
to pay such Rents without any inquiry into whether there exists an Event of
Default or whether Assignee is otherwise entitled to such Rents. Assignor hereby
waives any right, claim or demand which Assignor may now or hereafter have
against any present or future tenant, lessee or licensee by reason of such
payment of Rents to Assignee, and any such payment shall discharge such
tenant's, lessee's or licensee's obligation to make such payment to Assignor.

         13. Assignee may take or release any security for the Obligations, may
release any party primarily or secondarily liable for the Obligations, may grant
extensions, renewals or indulgences with respect to the Obligations and may
apply any other security therefore held by it to the satisfaction of any of the
Obligations without prejudice to any of its rights hereunder.

         14. The acceptance of this Assignment and the collection of the Rents
in the event Assignor's license is terminated, as referred to above, shall be
without prejudice to Assignee. The rights of Assignee hereunder are cumulative
and concurrent, may be pursued separately, successively or together and may be
exercised as often as occasion therefore shall arise, it being agreed by
Assignor that the exercise of any one or more of the rights provided for herein
shall not be construed as a waiver of any of the other rights or remedies of
Assignee, at law or in equity or otherwise, so long as any obligation under the
Subordinated Loan Documents remains unsatisfied.

         15. This Assignment shall be in full force and effect continuously from
the date hereof to and until all of the Obligations have been indefeasibly paid
and otherwise fully performed and satisfied.

         16. In addition to, but not in lieu of, any other rights hereunder,
Assignee shall have the right to institute suit and obtain a protective or
mandatory injunction against Assignor to prevent a breach or default, or to
enforce the observance, of the agreements, covenants, terms and conditions
contained herein, as well as the right to damages occasioned by any breach or
default by Assignor.

         17. This Assignment shall continue and remain in full force and effect
during any period of foreclosure with respect to the Mortgaged Property.

         18. Assignor hereby covenants and agrees that Assignee shall be
entitled to all of the rights, remedies and benefits available by statute, at
law, in equity or as a matter of practice for the enforcement and perfection of
the intents and purposes hereof. To the extent permitted by applicable law,
Assignee shall, as a matter of absolute right and without regard to the adequacy
of the security under the Loan Documents, be entitled, upon application to a
court of applicable jurisdiction and without further notice, to the appointment
of a receiver to obtain and secure the rights of Assignee hereunder and the
benefits intended to be provided to Assignee hereunder.



                                      -6-
<PAGE>

         19. This Assignment shall be construed and enforced in accordance with
the laws of the State of Florida, without application of its conflict of law
principles.

         20. Nothing in this Assignment shall ever be construed as subordinating
the Subordinated Loan Documents to any Lease; provided, however, that any
proceeding by Assignee to foreclose its liens encumbering the Mortgaged
Property, enforce any other remedy contained in the Loan Documents, or any
action by way of entry into possession after default, shall not operate to
terminate any Lease unless Assignee elects in writing to do so or unless the
tenant is named as a defendant in Assignee's foreclosure action.

         21. This Assignment shall not constitute or evidence any payment
whatsoever on account of the Obligations, and the Obligations shall be reduced
only to the extent of cash payments actually paid to Assignee and applied by
Assignee in reduction of the unpaid balance thereof.

         22. This Assignment is subordinate and subject to that certain
Assignment of Leases and Rents and Security Deposits dated as of September 5,
2001, made by and between Assignor and Ocean Bank, a Florida banking corporation
(the "Senior Assignment").



                                      -7-
<PAGE>


         IN WITNESS WHEREOF, Assignor has executed this Assignment as of the day
and year first above written.

Signed, sealed and delivered                  NAP OF THE AMERICAS, INC.,
in the presence of:                           a Delaware corporatino

                                              By: /s/ JOSE SEGRERA
                                                 -------------------------------
By: /s/ R. D. SICHTA                          Name:  Jose Segrera
   --------------------------                 Title: Vice President
Name:  R. D. Sichta
Title: Assistant Secretary


STATE OF FLORIDA
COUNTY OF MIAMI-DADE

         The foregoing instrument was acknowledged before me this 30th day of
April, 2003, by ______________, as__________________ of NAP OF THE AMERICAS,
INC., a Florida corporation on behalf of that corporation.

                                  Personally Known ____________ OR
                                  Produced Identification__________
                                  Type of Identification
                                  Produced____________________
                                  Signature:
                                             ----------------------------------

                                  Name: [Print or type]

                                  ---------------------------------------------

                                  Title: Notary Public
                                  Serial No., if any:
                                                     --------------------------

                                  My commission expires:



                                      -8-
<PAGE>


                                    EXHIBIT A


                                LEGAL DESCRIPTION

         Lots 1 through 20, inclusive, in Block 38 North, City of Miami,
according to the Plat thereof, as recorded in Plat Book B, Page 41, Public
Records of Miami-Dade County, Florida.











                                      -9-