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                                                                    EXHIBIT 4.2

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                              GREYHOUND LINES, INC.

                                       and

                           THE GUARANTOR NAMED HEREIN

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                              SERIES A AND SERIES B
                         11 1/2 % SENIOR NOTES DUE 2007

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                          FOURTH SUPPLEMENTAL INDENTURE

                            DATED AS OF MAY 14, 1999

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                       CHASE MANHATTAN TRUST COMPANY, N.A.
                                     Trustee


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        This FOURTH SUPPLEMENTAL INDENTURE, dated as of May 14, 1999, among
Greyhound Lines, Inc., a Delaware corporation (the "Company"), the party
identified under the caption "Guarantor" on the signature pages hereto (the
"Guarantor") and Chase Manhattan Trust Company, N.A. (successor to PNC Bank,
National Association), as Trustee.

                                    RECITALS

        WHEREAS, the Company and PNC Bank, National Association entered into an
Indenture, dated as of April 16, 1997 (the "Indenture"), pursuant to which the
Company issued $150,000,000 in principal amount of 11 1/2% Senior Notes due 2007
(the "Notes"); and

        WHEREAS, Section 9.01(e) of the Indenture provides that the Company and
the Trustee may amend or supplement the Indenture in order to execute a
guarantee (a "Subsidiary Guarantee") to comply with Section 10.02 thereof
without the consent of the Holders of the Notes; and

        WHEREAS, all acts and things prescribed by the Indenture, by law and by
the Certificate of Incorporation and the Bylaws of the Company, of the Guarantor
and of the Trustee necessary to make this Fourth Supplemental Indenture a valid
instrument legally binding on the Company, the Guarantor and the Trustee, in
accordance with its terms, have been duly done and performed;

        NOW, THEREFORE, to comply with the provisions of the Indenture and in
consideration of the above premises, the Company, the Guarantor and the Trustee
covenant and agree for the equal and proportionate benefit of the respective
Holders of the Notes as follows:

                                    ARTICLE I

        SECTION 1.01. This Fourth Supplemental Indenture is supplemental to the
Indenture and does and shall be deemed to form a part of, and shall be construed
in connection with and as part of, the Indenture for any and all purposes.

        SECTION 1.02. This Fourth Supplemental Indenture shall become effective
immediately upon its execution and delivery by each of the Company, the
Guarantor and the Trustee.

                                    ARTICLE 2

        From this date, in accordance with Section 10.02 and by executing this
Fourth Supplemental Indenture and the accompanying Subsidiary Guarantee (a copy
of which is attached hereto), the Guarantor whose signature appears below is
subject to the provisions of the Indenture to the extent provided for in Article
10 thereunder.


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                                    ARTICLE 3

        SECTION 3.01. Except as specifically modified herein, the Indenture and
the Notes are in all respects ratified and confirmed (mutatis mutandis) and
shall remain in full force and effect in accordance with their terms with all
capitalized terms used herein without definition having the same respective
meanings ascribed to them as in the Indenture.

        SECTION 3.02. Except as otherwise expressly provided herein, no duties,
responsibilities or liabilities are assumed, or shall be construed to be
assumed, by the Trustee by reason of this Fourth Supplemental Indenture. This
Fourth Supplemental Indenture is executed and accepted by the Trustee subject to
all the terms and conditions set forth in the Indenture with the same force and
effect as if those terms and conditions were repeated at length herein and made
applicable to the Trustee with respect hereto.

        SECTION 3.03. THE INTERNAL LAW OF THE STATE OF NEW YORK SHALL GOVERN AND
BE USED TO CONSTRUE THIS FOURTH SUPPLEMENTAL INDENTURE, THE NOTES AND THE
SUBSIDIARY GUARANTEES.

        SECTION 3.04. The parties may sign any number of copies of this Fourth
Supplemental Indenture. Each signed copy shall be an original, but all of such
executed copies together shall represent the same agreement.

        IN WITNESS WHEREOF, the parties hereto have caused this Fourth
Supplemental Indenture to be duly executed, all as of the date first written
above.

                                            GREYHOUND LINES, INC.


                                            By:
                                                -------------------------------
                                                Name:  Craig R. Lentzsch
                                                Title: President and CEO

                                            GUARANTOR:

                                            LSX DELIVERY, L.L.C.


                                            ON TIME DELIVERY SERVICE, INC.


                                            By:
                                                -------------------------------
                                                Name:  Jeffrey W. Sanders
                                                Title: Chief Financial Officer


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                                            CHASE MANHATTAN
                                            TRUST COMPANY, N.A.
                                            AS TRUSTEE


                                            By:
                                                -------------------------------
                                                Name:
                                                Title:


                                        3
<PAGE>   5

                                                          Attachment to Fourth
                                                          Supplemental Indenture


                              SUBSIDIARY GUARANTEE

        Subject to Section 10.06 of the Indenture, the undersigned Guarantor
hereby unconditionally guarantees to each Holder of a Note authenticated and
delivered by the Trustee and to the Trustee and its successors and assigns,
irrespective of the validity and enforceability of the, Indenture, the Notes and
the Obligations of the Company under the Notes or under the Indenture, that: (a)
the principal of, premium, if any, interest and Liquidated Damages, if any, on
the Notes will be promptly paid in full when due, subject to any applicable
grace period, whether at maturity, by acceleration, redemption or otherwise, and
interest on overdue principal, premium, if any, (to the extent permitted by law)
interest on any interest, if any, and Liquidated Damages, if any, on the Notes
and all other payment Obligations of the Company to the Holders or the Trustee
under the Indenture or under the Notes will be promptly paid in full and
performed, all in accordance with the terms thereof; and (b) in case of any
extension of time of payment or renewal of any Notes or any of such other
payment Obligations, the same will be promptly paid in full when due or
performed in accordance with the terms of the extension or renewal, subject to
any applicable grace period, whether at stated maturity, by acceleration,
redemption or otherwise. Failing payment when so due of any amount so guaranteed
or any performance so guaranteed for whatever reason, the Guarantor will be
obligated to pay the same immediately. An Event of Default under the Indenture
or the Notes shall constitute an event of default under this Subsidiary
Guarantee, and shall entitle the Holders to accelerate the Obligations of the
Guarantor hereunder in the same manner and to the same extent as the Obligations
of the Company. The Guarantor hereby agrees that its Obligations hereunder shall
be unconditional, irrespective of the validity, regularity or enforceability of
the Notes or the Indenture, the absence of any action to enforce the same, any
waiver or consent by any Holder with respect to any provisions hereof or
thereof, the recovery of any judgment against the Company, any action to enforce
the same or any other circumstance which might otherwise constitute a legal or
equitable discharge or defense of the Guarantor. The Guarantor hereby waives
diligence, presentment, demand of payment, filing of claims with a court in the
event of insolvency or bankruptcy of the Company, any right to require a
proceeding first against the Company, protest, notice and all demands whatsoever
and covenants that this Subsidiary Guarantee will not be discharged except by
complete performance of the Obligations contained in the Notes and the
Indenture. If any Holder or the Trustee is required by any court or otherwise to
return to the Company, the Guarantor, or any Note Custodian, Trustee, liquidator
or other similar official acting in relation to either the Company or the
Guarantor, any amount paid by the Company or the Guarantor to the Trustee or
such Holder, this Subsidiary Guarantee, to the extent theretofore discharged,
shall be reinstated in full force and effect. The Guarantor agrees that it shall
not be entitled to, and hereby waives, any right of subrogation in relation to
the Holders in respect of any Obligations guaranteed hereby. The Guarantor
further agrees that, as between the Guarantor, on the one hand, and the Holders
and the Trustee, on the other hand, (a) the maturity of the Obligations
guaranteed hereby may be accelerated as provided in Article 6 of the Indenture
for the purposes of this Subsidiary Guarantee, notwithstanding any stay,
injunction or other prohibition preventing such acceleration in respect of the
Obligations guaranteed thereby, and (b)


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in the event of any declaration of acceleration of such Obligations as provided
in Article 6 of the Indenture, such Obligations (whether or not due and payable)
shall forthwith become due and payable by the Guarantor for the purpose of this
Subsidiary Guarantee. The Guarantor shall have the right to seek contribution
from any non-paying Guarantor so long as the exercise of such right does not
impair the rights of the Holders under the Subsidiary Guarantees.

                The obligations of the Guarantor to the Holders and to the
Trustee pursuant to this Subsidiary Guarantee and the Indenture are expressly
set forth in Article 10 of the Indenture, and reference is hereby made to such
Indenture for the precise terms of this Subsidiary Guarantee. The terms of
Article 10 of the Indenture are incorporated herein by reference. This
Subsidiary Guarantee is subject to release as and to the extent provided in
Sections 10.04 and 10.05 of the Indenture.

                This is a continuing Guarantee and shall remain in full force
and effect and shall be binding upon the Guarantor and its respective successors
and assigns to the extent set forth in the Indenture until full and final
payment of all of the Company's Obligations under the Notes and the Indenture
and shall inure to the benefit of the successors and assigns of the Trustee and
the Holders and, in the event of any transfer or assignment of rights by any
Holder or the Trustee, the rights and privileges herein conferred upon that
party shall automatically extend to and be vested in such transferee or
assignee, all subject to the terms and conditions hereof. This is a Subsidiary
Guarantee of payment and not a guarantee of collection.

                This Subsidiary Guarantee shall not be valid or obligatory for
any purpose until the certificate of authentication on the Note upon which this
Subsidiary Guarantee is noted shall have been executed by the Trustee or an
authenticating agent under the Indenture by the manual signature of one of its
authorized officers.

                For purposes hereof, the Guarantor's liability shall be limited
to the lesser of (i) the aggregate amount of the Obligations of the Company
under the Notes and the Indenture and (ii) the amount, if any, which would not
have (A) rendered the Guarantor "insolvent" (as such term is defined in the
Bankruptcy Law and in the Debtor and Creditor Law of the State of New York) or
(B) left the Guarantor with unreasonably small capital at the time its
Subsidiary Guarantee of the Notes was entered into; provided that, it will be a
presumption in any lawsuit or other proceeding in which the Guarantor is a party
that the amount guaranteed pursuant to the Subsidiary Guarantee is the amount
set forth in clause (i) above unless any creditor, or representative of
creditors of the Guarantor, or debtor in possession or trustee in bankruptcy of
the Guarantor, otherwise proves in such a lawsuit that the aggregate liability
of the Guarantor is limited to the amount set forth in clause (ii) above. The
Indenture provides that, in making any determination as to the solvency or
sufficiency of capital of the Guarantor in accordance with the previous
sentence, the right of the Guarantor to contribution from other Guarantors and
any other rights such Guarantors may have, contractual or otherwise, shall be
taken into account.


                                        2

<PAGE>   7


                Capitalized terms used herein have the same meanings given in
the Indenture unless otherwise indicated.

                                             [GUARANTOR]

                                            By:
                                                -------------------------------
                                                Name:
                                                Title:


                                        3
<PAGE>   8


                              SUBSIDIARY GUARANTEE

        Subject to Section 10.06 of the Indenture, the undersigned Guarantor
hereby unconditionally guarantees to each Holder of a Note authenticated and
delivered by the Trustee and to the Trustee and its successors and assigns,
irrespective of the validity and enforceability of the, Indenture, the Notes and
the Obligations of the Company under the Notes or under the Indenture, that: (a)
the principal of, premium, if any, interest and Liquidated Damages, if any, on
the Notes will be promptly paid in full when due, subject to any applicable
grace period, whether at maturity, by acceleration, redemption or otherwise, and
interest on overdue principal, premium, if any, (to the extent permitted by law)
interest on any interest, if any, and Liquidated Damages, if any, on the Notes
and all other payment Obligations of the Company to the Holders or the Trustee
under the Indenture or under the Notes will be promptly paid in full and
performed, all in accordance with the terms thereof; and (b) in case of any
extension of time of payment or renewal of any Notes or any of such other
payment Obligations, the same will be promptly paid in full when due or
performed in accordance with the terms of the extension or renewal, subject to
any applicable grace period, whether at stated maturity, by acceleration,
redemption or otherwise. Failing payment when so due of any amount so guaranteed
or any performance so guaranteed for whatever reason, the Guarantor will be
obligated to pay the same immediately. An Event of Default under the Indenture
or the Notes shall constitute an event of default under this Subsidiary
Guarantee, and shall entitle the Holders to accelerate the Obligations of the
Guarantor hereunder in the same manner and to the same extent as the Obligations
of the Company. The Guarantor hereby agrees that its Obligations hereunder shall
be unconditional, irrespective of the validity, regularity or enforceability of
the Notes or the Indenture, the absence of any action to enforce the same, any
waiver or consent by any Holder with respect to any provisions hereof or
thereof, the recovery of any judgment against the Company, any action to enforce
the same or any other circumstance which might otherwise constitute a legal or
equitable discharge or defense of the Guarantor. The Guarantor hereby waives
diligence, presentment, demand of payment, filing of claims with a court in the
event of insolvency or bankruptcy of the Company, any right to require a
proceeding first against the Company, protest, notice and all demands whatsoever
and covenants that this Subsidiary Guarantee will not be discharged except by
complete performance of the Obligations contained in the Notes and the
Indenture. If any Holder or the Trustee is required by any court or otherwise to
return to the Company, the Guarantor, or any Note Custodian, Trustee, liquidator
or other similar official acting in relation to either the Company or the
Guarantor, any amount paid by the Company or the Guarantor to the Trustee or
such Holder, this Subsidiary Guarantee, to the extent theretofore discharged,
shall be reinstated in full force and effect. The Guarantor agrees that it shall
not be entitled to, and hereby waives, any right of subrogation in relation to
the Holders in respect of any Obligations guaranteed hereby. The Guarantor
further agrees that, as between the Guarantor, on the one hand, and the Holders
and the Trustee, on the other hand, (a) the maturity of the Obligations
guaranteed hereby may be accelerated as provided in Article 6 of the Indenture
for the purposes of this Subsidiary Guarantee, notwithstanding any stay,
injunction or other prohibition preventing such acceleration in respect of the
Obligations guaranteed thereby, and (b) in the event of any declaration of
acceleration of such Obligations as provided in Article 6 of the Indenture, such
Obligations (whether or not due and payable) shall forthwith become due and
payable by the Guarantor for the purpose of this Subsidiary Guarantee. The
Guarantor shall have


<PAGE>   9


the right to seek contribution from any non-paying Guarantor so long as the
exercise of such right does not impair the rights of the Holders under the
Subsidiary Guarantees.

                The obligations of the Guarantor to the Holders and to the
Trustee pursuant to this Subsidiary Guarantee and the Indenture are expressly
set forth in Article 10 of the Indenture, and reference is hereby made to such
Indenture for the precise terms of this Subsidiary Guarantee. The terms of
Article 10 of the Indenture are incorporated herein by reference. This
Subsidiary Guarantee is subject to release as and to the extent provided in
Sections 10.04 and 10.05 of the Indenture.

                This is a continuing Guarantee and shall remain in full force
and effect and shall be binding upon the Guarantor and its respective successors
and assigns to the extent set forth in the Indenture until full and final
payment of all of the Company's Obligations under the Notes and the Indenture
and shall inure to the benefit of the successors and assigns of the Trustee and
the Holders and, in the event of any transfer or assignment of rights by any
Holder or the Trustee, the rights and privileges herein conferred upon that
party shall automatically extend to and be vested in such transferee or
assignee, all subject to the terms and conditions hereof. This is a Subsidiary
Guarantee of payment and not a guarantee of collection.

                This Subsidiary Guarantee shall not be valid or obligatory for
any purpose until the certificate of authentication on the Note upon which this
Subsidiary Guarantee is noted shall have been executed by the Trustee or an
authenticating agent under the Indenture by the manual signature of one of its
authorized officers.

                For purposes hereof, the Guarantor's liability shall be limited
to the lesser of (i) the aggregate amount of the Obligations of the Company
under the Notes and the Indenture and (ii) the amount, if any, which would not
have (A) rendered the Guarantor "insolvent" (as such term is defined in the
Bankruptcy Law and in the Debtor and Creditor Law of the State of New York) or
(B) left the Guarantor with unreasonably small capital at the time its
Subsidiary Guarantee of the Notes was entered into; provided that, it will be a
presumption in any lawsuit or other proceeding in which the Guarantor is a party
that the amount guaranteed pursuant to the Subsidiary Guarantee is the amount
set forth in clause (i) above unless any creditor, or representative of
creditors of the Guarantor, or debtor in possession or trustee in bankruptcy of
the Guarantor, otherwise proves in such a lawsuit that the aggregate liability
of the Guarantor is limited to the amount set forth in clause (ii) above. The
Indenture provides that, in making any determination as to the solvency or
sufficiency of capital of the Guarantor in accordance with the previous
sentence, the right of the Guarantor to contribution from other Guarantors and
any other rights such Guarantors may have, contractual or otherwise, shall be
taken into account.


                                       E-2
<PAGE>   10


        Capitalized terms used herein have the same meanings given in the
Indenture unless otherwise indicated.


                                            GUARANTOR:

                                            LSX DELIVERY, L.L.C.


                                            By:
                                                -------------------------------
                                                Name:  Jeffrey W. Sanders
                                                Title: Chief Financial Officer


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