<PAGE>

                                                                    EXHIBIT 10.6

                              (On AET lefterhead)
                              -------------------

                             Guarantee Fee Letter
                             --------------------

Date: 5th June 2001


Neptune Orient Lines Limited
456 Alexandra Road,
#06-00, NOL Building
Singapore 119962


Attention:  Mr Lim How Teck
            Group Chief Financial Officer


Dear Sir,


Guarantee Fees
--------------

We refer to the guarantees of Neptune Orient Lines Limited ("NOL) guaranteeing
in favour of Lenders our (and/or our subsidiaries) outstanding payment
obligations to them under several loan facilities.

A schedule of the guaranteed loan facilities as at the date of this letter
agreement is attached hereto as Appendix 1 (the "Loan Facilites"). We have
agreed that this schedule may be subject to our mutual amendment, variation or
addition from time to time.

Following and consequent to our successful initial public offering ("IPO"), we
shall pay to NOL a guarantee fee calculated at 0.125% per annum of the
outstanding payments owing by us (and/or our subsidiaries) to the Lenders under
the terms of the Loan Facilities up to the amount which NOL has guaranteed (the
"Guaranteed Debt"). This guarantee fee shall be paid net of any taxes,
withholding or otherwise, which taxes shall be to our account.

The guarantee fee shall be paid quarterly in arrears (0.03125% per quarter) and
the first quarterly payment shall be on a date six months from the IPO. The
quantum of the Guaranteed Debt shall be determined between us in good faith from
time to time and in any event such determination must take place no later than
one week before our guarantee fee payment becomes due.

We have agreed with NOL that no guarantee fee shall be payable on any Guaranteed
Debt for any period before the IPO.
<PAGE>

                                       2
NOL has agreed that it shall continue to guarantee our (and/or our subsidiaries)
payment obligations under the stated loan facilities so long as we pay the
guarantee fee to NOL in accordance with the terms of this letter agreement, save
insofar as such guarantees are no longer required by the Lenders in accordance
with the terms of the Loan Facilities or NOL guarantees.

The terms of this letter agreement shall be construed and governed in accordance
with Singapore law.

If the above correctly sets out our agreement, please indicate your acceptance
of the terms of this letter by your acknowledgement below.


Yours sincerely,


JOSEPH KWOK
President and CEO
American Eagle Tankers Inc. Limited



We, Neptune Orient Lines Limited, hereby acknowledge our acceptance to the terms
and conditions of this letter agreement.

LIM HOW TECK
Group Chief Financial Officer
Neptune Orient Lines Limited.
<PAGE>

                                       3



                                  APPENDIX 1

Guaranteed Loan Facilities:


   (i)   One (1) loan facility between The Development Bank of Singapore and AET
         dated 5th March 2001

   (ii)  Two (2) loan facilities between Lepta Shipping Co Ltd and AET both
         dated 21st February 2001

   (iii) One (1) loan facility between Trilithon Shipping Pte Ltd and Dai Ichi
         Kangyou Bank Ltd as Facility Agent & syndicate dated 31st March 1995
         (See footnote (a))

   (iv)  One (1) loan facility between Trilith Shipping Pte Ltd and Tokyo
         Mitsubishi International (Spore) Ltd as Facility Agent & syndicate
         dated 29th March 1995 (See footnote (b))

   (v)   One (1) loan facility between Crystal Shipowning Co. Pte Ltd and OCBC
         Bank dated 6th April 1994 (See footnote (c)).


Footnotes:

        (a)  NOL guarantees 65% of this loan and the Guaranteed Debt shall be so
             construed.

        (b)  NOL guarantees 65% of this loan and the Guaranteed Debt shall be so
             construed.

        (c)  NOL guarantees 100% of this loan with a counter indemnity of 35%
             from Mitsui & Co. The Guaranteed Debt shall be construed on the
             basis of 65%.