<PAGE>   1
                                                                       EXHIBIT 1



                                 TERMS AGREEMENT

     August 31, 1999

Aristar, Inc.
1201 Third Avenue
Suite 1500
Seattle, Washington 98101

Dear Sirs:

     We (the "Underwriters" and the  "Representative")  understand that Aristar,
Inc.,  a Delaware  corporation  (the  "Company"),  proposes  to issue and sell
$300,000,000  aggregate principal amount of its 7-3/8% Senior Notes due
September 1, 2004 (the "Underwritten Securities"). Subject to the terms and
conditions set forth herein or incorporated by reference herein, the
Underwriters  hereby offer to purchase,  severally and not jointly,  the
principal  amount of  Underwritten Securities  set forth opposite  their
respective  names below at 99.071% of the principal amount thereof.

<TABLE>
<CAPTION>
                                                                 Principal
                    Underwriters                                  Amount
                    ------------                              ------------
<S>                                                           <C>
     Banc One Capital Markets, Inc.........................   $120,000,000
     First Union Capital Markets Corp......................    120,000,000
     ABN AMRO Incorporated.................................     24,000,000
     Nesbitt Burns Securities Inc..........................     24,000,000
     BNY Capital Markets, Inc..............................      6,000,000
     Mellon Financial Markets Inc..........................      6,000,000
                                                              ------------
                       Total ..............................   $300,000,000
                                                              ============
</TABLE>


          The Underwritten Securities shall have the following terms:

<TABLE>
<S>                            <C>
Date of maturity:              September 1, 2004

Interest rate:                 7-3/8% per annum, payable semiannually

Initial public offering price: 99.621%

Interest payment dates:        September 1st  and March 1st, commencing March 1, 2000

Redemption provisions:         The Underwritten Securities are not redeemable

Form:                          The Underwritten Securities are to be issued in the form of
                               one or more global securities registered in the name of The
                               Depository Trust Company or its nominee (the "Depositary");
                               delivery of the Underwritten Securities at closing will be
                               made through the facilities of the Depositary

Specified funds for payment
  of purchase price:           Wire transfer of immediately available funds
</TABLE>


<PAGE>   2

<TABLE>
<S>                            <C>
Specified address for notices: Banc One Capital Markets, Inc.
                               One First National Plaza
                               Suite IL1-0595
                               Chicago, Illinois 60670
                               Attention: Corporate Securities Structuring

Delivery Date:                 11:00 A.M., New York City time, on September 7, 1999

Place of closing:              Simpson Thacher & Bartlett
                               425 Lexington Avenue
                               New York, New York  10017
</TABLE>


     The Underwriters hereby confirm that they have furnished to the Company in
writing the following information for inclusion in the Company's Prospectus
Supplement dated August 31, 1999 to the Company's Prospectus dated June 22, 1999
relating to the Underwritten Securities (the "Prospectus Supplement"): (i) the
table on page S-8 of the Prospectus Supplement, (ii) the second paragraph below
the table on page S-8 of the Prospectus Supplement concerning the public
offering price, concession and discount; (iii) the third and fourth sentences of
the fourth paragraph below the table on page S-8 of the Prospectus Supplement;
(iv) the sixth paragraph below the table on page S-8 of the Prospectus
Supplement concerning over-allotment, stabilizing transactions, syndicate
covering transactions and penalty bids; and (v) the fifth and sixth sentences of
the seventh paragraph below the table on page S-8 of the Prospectus Supplement.

     All of the provisions contained in the document entitled "Aristar, Inc. --
Debt Securities -- Underwriting Agreement Basic Provisions" and dated June 23,
1999 (the "Basic Provisions"), a copy of which you have previously furnished to
us, are herein incorporated by reference in their entirety and shall be deemed
to be a part of this Terms Agreement to the same extent as if such provisions
had been set forth in full herein; provided, however, that

     (i) subparagraph (iv) of clause (c) of Paragraph 9 of such provisions shall
be deleted and shall be replaced in its entirety by the following: "(iv) The
Underwritten Securities and the Indenture conform in all material respects to
the statements concerning them contained on the cover page of the Prospectus and
of the Basic Prospectus and in the sections entitled "Certain Terms of the
Notes" in the Prospectus and entitled "Description of Debt Securities" in the
Basic Prospectus."

     Terms defined in such Underwriting Agreement Basic Provisions are used
herein as therein defined.

<PAGE>   3

     Please accept this offer no later than 11:00 P.M., New York City time, on
August 31, 1999 by signing a copy of this Terms Agreement in the space set forth
below and returning the signed copy to us, or by sending us a written acceptance
in the following form:

     "We hereby accept your offer, set forth in the Terms Agreement dated August
31, 1999, to purchase the Underwritten Securities on the terms set forth
therein."

                                        Very truly yours,

                                        BANC ONE CAPITAL MARKETS, INC.
                                        FIRST UNION CAPITAL MARKETS CORP.
                                        ABN AMRO INCORPORATED
                                        NESBITT BURNS SECURITIES INC.
                                        BNY CAPITAL MARKETS, INC.
                                        MELLON FINANCIAL MARKETS INC.


                                        By: BANC ONE CAPITAL MARKETS, INC.

                                            By: /s/ Jeffrey W. Kolb
                                                --------------------------------
                                            (Banc One Capital Markets, Inc.)
                                                Name: Jeffrey W. Kolb
                                                Title: Managing Director


                                        By: FIRST UNION CAPITAL MARKETS CORP.


                                            By: /s/ Keith J. Mauney
                                                --------------------------------
                                            (First Union Capital Markets Corp.)
                                                Name: Keith J. Mauney
                                                Title: Managing Director


Accepted:

Aristar, Inc.

By: /s/ Fay Chapman
    -------------------------------
    Name:  Fay Chapman
    Title: Executive Vice President