<PAGE>

                                                                   EXHIBIT 10.18

                               SUPPLY AGREEMENT
                               ----------------

          THIS IS A SUPPLY AGREEMENT dated as of the 30th day of March, 1992
(the "Agreement"), between CONE MILLS CORPORATION, a North Carolina corporation
("Cone"), and LEVI STRAUSS & CO., a Delaware corporation ("LS&CO.").

          WHEREAS, Cone is a major supplier of LS&CO. and LS&CO. is Cone's
largest customer; and

          WHEREAS, Cone and LS&CO. have maintained, for more than 75 years, a
unique, cooperative supplier/customer relationship for the development of Cone
XXX denim fabrics used in the LS&CO. 501(R) family of jeans, a relationship
premised in part on management compatibility and continuity; and

          WHEREAS, Cone and LS&CO. desire to solidify their relationship and
assure its continuity;

          NOW, THEREFORE, in consideration of the premises and other good and
valuable consideration, receipt of which is acknowledged, it is agreed:

          1.   Definitions.  For purposes of this Agreement, the following terms
               -----------
shall have the definitions indicated:

          1.1  "Change in Control" means the occurrence of any of the following
               events:

               (a)  the individuals who at the date of this Agreement comprise
                    the members of the Cone Board of Directors (together with
                    any new director whose election by the Board of Directors or
                    whose nomination for election by the company's shareholders
                    was approved by a majority of the directors then still in
                    office who were directors at the date of this Agreement or
                    who were nominated by them) shall cease for any reason to
                    comprise at least a majority of the members of the Board of
                    Directors;

               (b)  Cone consolidates with or merges into any other corporation
                    or any corporation consolidates with or merges into Cone, or
                    Cone becomes a subsidiary of another corporation, if, after
                    giving effect to the transaction, the holders of Cone's
                    voting securities immediately before the


<PAGE>

                    effective date of the transaction hold less than 50% of the
                    voting securities of the surviving or parent corporation; or


               (c)  any person (other than any person who is a director or
                    stockholder of Cone at the date of this Agreement, Cone, a
                    subsidiary of Cone or a Cone employee benefit plan,
                    including any trustee of such a plan acting as trustee)
                    shall purchase or otherwise acquire or hold beneficial
                    ownership of securities of Cone and, as a result of those
                    purchases and acquisitions, directly or indirectly
                    beneficially owns in the aggregate securities of Cone
                    representing 50% or more of Cone's then outstanding voting
                    securities (it being understood that the terms "person" and
                    "beneficial ownership" used in this paragraph 1.1(c) have
                    the meanings given them in Sections 13 (d) and 14 and Rule
                    13d 3, respectively, of and under the Securities Exchange
                    Act of 1934, as amended (the "Exchange Act")).

          1.2  "Contract Price" means, at any point in time, the average market
               price per yard then being paid by LS&CO. in the ordinary course
               of business (excluding special arrangements not in effect on the
               date of this Agreement and not generally prevailing in the
               market) for indigo denim of comparable weight and color purchased
               for all jeans applications excluding the 501(R) jeans family,
               plus a percentage premium which has been paid for 501(R) jeans
               fabric over and above the average price for the aforementioned
               fabrics for the immediately preceding sixteen (16) calendar
               quarters.

          1.3  "Order Documentation" means the purchase orders, confirmations of
               sales, invoices and other documents currently used by Cone and
               LS&CO. in documenting orders by, and shipments to, LS&CO., of XXX
               Denim, the forms of which are attached as Exhibit A to this
                                                         --------
               Agreement.

          1.4  "White Oak Plant" means Cone's facility known as the White Oak
               Plant located on Fairview Street in Greensboro, North Carolina,
               including the real property, machinery and equipment and
               furnishings and fixtures and service functions located at such
               facility.

          1.5  "Vendor Certification Requirements" means the quality, service
               and fabric construction qualifications established in writing by
               LS&CO. for its vendors from time to time.

                                       2
<PAGE>

          1.6  "XXX Denim" means any and all denim fabric of the construction
               and physical characteristics which has been approved by LS&CO. in
               its Vendor Certification Program for use, or is in fact used, in
               the 501(R) family of jeans.

          2.   Requirements Agreement
               ----------------------

          2.1  Generally: LS&CO. agrees to purchase from Cone, and Cone agrees
               to manufacture and sell to LS&CO., all XXX Denim that may be
               required by LS&CO. in its business. Cone shall not sell, or
               otherwise make XXX Denim available, to any person other than
               LS&CO., and LS&CO. shall not purchase, or otherwise obtain XXX
               Denim from, any other source than Cone, during the term of the
               obligations created by this Section 2; that is, this is an
               "exclusive" agreement on the part of both LS&CO. and Cone.

          2.2  Ordering and Pricing:  Cone shall deliver XXX Denim to LS&CO. in
               accordance with specific orders placed by LS&CO. Cone and LS&CO.
               shall document those orders and deliveries by use of, and their
               terms (including, without limitation, those relating to
               warranties, remedies and shipment terms and except as otherwise
               set forth in this Agreement) shall be governed by, the Order
               Documentation. Cone and LS&CO. shall determine the price for a
               specific delivery at or before the time LS&CO. places the order
               for that delivery, it being understood that Cone and LS&CO.
               intend to be bound in respect of and to conclude these specific
               sales even though the price for specific sales is not settled as
               of the date of this Agreement.

          2.3  Term:  The obligations of Cone and LS&CO. under this Section 2
               shall continue until the termination of those obligations in
               accordance with Section 3 or 5 of this Agreement. A Change in
               Control shall not of itself impair, limit or affect or limit
               those obligations, in any respect, unless and until LS&CO.
               provides to Cone the written notice contemplated by Section 3.2
               of this Agreement.

          3.   Change in Control
               -----------------

          3.1  Generally: For a period of one year from and after a Change in
               Control, LS&CO. may elect to terminate the requirements
               obligation established by Section 2 of this Agreement and
               implement an alternative, "wind-down" arrangement on the terms
               and conditions set forth in this Section 3, it being understood
               that

                                       3
<PAGE>

               this one-year period may, at LS&CO.'s option, be treated as not
               "running" until LS&CO. receives notice from Cone of a Change in
               Control as contemplated by Section 11 of this Agreement.

          3.2  Commencement and Term:  The termination of Section 2 and the
               alternative arrangement established by this Section 3 shall
               become effective on the date Cone receives a written notice to
               that effect from LS&CO., and shall, unless terminated in
               accordance with Section 5 of this Agreement, remain in effect for
               a period of three years after that notice is received by Cone.

          3.3  Quantity:  Cone shall be obligated to manufacture and sell to
               LS&CO. up to thirty million (30,000,000) yards of XXX Denim
               during each calendar quarter during the effective period
               described in Section 3.2, it being understood that this amount
               shall be prorated for any partial quarters. LS&CO. shall be
               obligated to purchase from Cone only those amounts of XXX Denim
               it orders, but shall have no "requirements" or minimum purchase
               obligation.

          3.4  Ordering:  Cone shall deliver XXX Denim to LS&CO. in accordance
               with specific orders placed by LS&CO. Cone and LS&CO. shall
               document those orders and deliveries by use of, and their terms
               including, without limitation, those relating to warranties,
               remedies and shipment terms and except as otherwise set forth in
               this Agreement) shall be governed by, the Order Documentation.

          3.5  Price:  The price per yard for XXX Denim sold under this Section
               3 will be the Contract Price as of the order date, calculated and
               effective. in accordance with the normal practice of the parties
               as it exists on the date of this Agreement. In addition, LS&CO.
               shall pay Cone an amount equal to 1.5% of the total purchase
               price of purchases by LS&CO. of XXX Denim for any calendar
               quarter in which LS&CO. purchases less than 15 million
               (15,000,000) yards of XXX Denim.

          3.6  Exclusivity:  During the effective period described in Section
               3.2 of this Agreement, and so long as LS&CO. purchases ten
               million (10,000,000) yards of XXX Denim per calendar quarter
               under this Section 3, Cone will sell XXX Denim exclusively to
               LS&CO.

          3.7  Later Change in Control:  A decision by LS&CO. not to elect to
               implement the alternative arrangement contemplated by this
               Section 3 within one year after a Change in Control shall not
               limit

                                       4
<PAGE>

               or otherwise affect its ability to so elect-following a later
               Change in Control.

          4.   Lease Option
               ------------

          4.1  Generally:  Subject to the provisions of Section 4.4 and Section
               5 of this Agreement, in the event that Cone fails to supply XXX
               Denim to LS&CO. in accordance with the provisions of Section 3 of
               this Agreement, LS&CO. may, at its option, lease, obtain
               possession of, operate and retain the output of the White Oak
               Plant, on the terms and conditions contained in this Section 4
               and in a lease agreement substantially in the form attached to
               this Agreement as Exhibit B. The term of the lease shall commence
                                 --------
               75 days after LS&CO. provides to Cone the option exercise notice
               contemplated by Section 4.2 of this Agreement, and shall expire
               on the fourth anniversary of the Change in Control giving rise to
               the establishment of the arrangement contemplated by Section 3 of
               this Agreement (the "Applicable Change in Control").

          4.2  Term and Exercise of Option:  The term of the option shall begin
               on the date of delivery by LS&CO. to Cone of the notice
               contemplated by Section 3.2 of this Agreement and shall expire
               upon the earlier of: (a) three years after that notice is
               received by Cone or (b) on the fourth anniversary of the
               Applicable Change in Control. If and after the option becomes
               exercisable as contemplated by Section 4.1 of this Agreement,
               LS&CO. may exercise it by delivering to Cone a written notice to
               that effect. Cone and LS&CO. agree to execute the lease agreement
               upon exercise by LS&CO. of its option.

          4.3  Cooperation:  Cone shall cooperate with LS&CO. and take such
               further actions as may be reasonably appropriate in order to
               enable LS&CO. to obtain XXX Denim through exercising its option,
               including, without limitation, maintaining the White Oak Plant in
               good repair and proper order, facilitating transition
               relationships with Cone's suppliers and other customers, and,
               after the Applicable Change in Control, permitting LS&CO. and its
               contractors, agents, employees, and permitted assigns to enter on
               and to inspect the  property, and to conduct such engineering,
               mechanical, environmental, and other investigations as they may
               reasonably desire, all to be performed at LS&CO.'s expense. Cone
               and LS&CO. shall annually review changes and proposed changes by
               Cone in the manufacturing capabilities of the White Oak Plant
               and, should Cone, in accordance with its management and financial
               policies and practices, shift XXX Denim manufacturing

                                       5
<PAGE>

               capacities such that LS&CO. could not obtain XXX Denim by
               operating the White Oak Plant as contemplated by Section 4.1 of
               this Agreement, LS&CO. and Cone shall negotiate in good faith to
               adjust, in an equitable manner, the provisions of this Section 4
               in order to provide LS&CO. with the ability to obtain XXX Denim
               by operating and retaining the output of such other facilities.
               Cone represents and warrants to LS&CO. that it is seized of the
               White Oak Plant in fee simple.

          4.4  Effectiveness:  Notwithstanding its provisions or any other
               provisions of this Agreement, this Section 4 shall not become
               effective until Cone obtains an appropriate waiver under, or a
               termination or appropriate amendment of, its Credit Agreement,
               dated as of April 17, 1989, among Cone, the lenders named therein
               and Morgan Guaranty Trust Company of New York, as Agent, Cone
               having advised LS&CO. that the Credit Agreement may restrict its
               ability to enter into the arrangement contemplated by this
               Section 4. Cone has further advised LS&CO. that it intends to and
               believes it will be able to obtain such a waiver, amendment or
               termination by December 31, 1992. Cone shall regularly inform
               LS&CO. about its efforts to obtain the consent, amendment or
               termination. Cone agrees to use its best efforts to obtain the
               consent, and further agrees that, subject to the next sentence of
               this Section 4.4, it shall not, during the term of this
               Agreement, enter into credit or other agreements that prohibit or
               limit its ability to enter into and perform the arrangement
               contemplated by this Section 4. Cone and LS&CO. further agree,
               however, that: (a) this Section 4.4 shall not prevent Cone from
               granting mortgages, deeds of trust or security interests in its
               properties and (b) that the provisions of this Section 4 shall be
               subject to and subordinate to any such mortgages, deeds of trust
               and security interests but that the effectiveness of any such
               subordination shall be subject to receipt by LS&CO. of
               appropriate non-disturbance agreements or assurances from the
               beneficiary of those security instruments, all as contemplated by
               Section 19 of the form of lease agreement attached to this
               Agreement as Exhibit B.
                            ---------

          5.   Termination
               -----------

          5.1  Generally:  This Agreement shall terminate upon the earlier of:
               (a) March 30, 1997, if LS&CO. does not deliver to Cone the notice
               contemplated by Section 3.2 of this Agreement, and as that
               expiration date may be extended as described in this Section 5.1;
               (b) if LS&CO. delivers to Cone the notice contemplated by Section
               3.2 of this Agreement, three years after the delivery of that


                                       6
<PAGE>

               notice; or (c) its termination in accordance with Sections 5.2 or
               5.3 of this Agreement. Unless this Agreement has or is to be
               terminated as described in clauses (b) and (c) of the preceding
               sentence, the term (that is, the expiration date) of this
               Agreement shall, upon March 30 of each year, be automatically
               extended by one year, unless Cone or LS&CO. provides written
               notice to the other, during the month of February of that year,
               of its desire not to extend the term (for example, if such notice
               of non-extension is not given in February 1993, the term of this
               Agreement shall automatically be extended to March 30, 1998). If
               notice of non-extension is given, the term of the Agreement shall
               expire on the then effective expiration date.

          5.2  Certain Events:  Either party, at its option and without
               prejudice to any other remedy to which it may be entitled either
               at law or in equity, may immediately terminate this Agreement by
               written notice to the other party on the occurrence of any of the
               following events: (i) the other party shall file a petition in
               bankruptcy or shall be adjudged a bankrupt; (ii) the other party
               shall file a petition in reorganization under the provisions of
               Federal or State bankruptcy laws; (iii) the other party shall
               become or be declared insolvent; (iv) a receiver of all or
               substantially all of the property of the other party shall be
               appointed and not removed within thirty days; (v) the other party
               shall make a general assignment for the benefit of its creditors;
               or (vi) there shall be a material breach by the other party of
               any provision of this Agreement or a substantial failure by the
               other party to perform one or more of its obligations under this
               Agreement, which shall not have been cured within fifteen (15)
               days after written notice specifying the nature of such breach or
               failure.

          5.3  Termination by LS&CO.:  LS&CO. may, upon thirty (30) days written
               notice to Cone, terminate its obligations under Section 2 for any
               reason or for no reason, but that act shall have the effect of
               terminating the entire Agreement including, without limitation,
               its Sections 3 and 4.

          5.4  Effect of Termination:  It is understood and agreed that, with
               respect to any termination of this Agreement, Cone and LS&CO.
               shall be bound to perform their obligations in respect of orders
               for XXX Denim outstanding as of the date of notice of termination
               or, in the case of termination by passage of time in accordance
               with clause (a) of Section 5.1, the date of termination.

                                       7
<PAGE>

          6.   Not Partners.  This Agreement does not constitute either party as
               ------------
an agent, partner, joint venturer or legal representative of the other for any
purpose whatsoever, it being understood between the parties that each is to act
as an independent party and is in no way authorized to make any agreement,
contract, or representation on behalf of the other, or to create any obligation,
express or implied, on behalf of the other.

          7.   Notices and Correspondence.  All notices which are required or
               --------------------------
permitted to be given pursuant to the terms of this Agreement must be in writing
and will be deemed to have been duly given and made only if: served by personal
delivery to the party for whom it is intended; delivered to an air courier
guaranteeing overnight delivery; or deposited, postage prepaid, certified or
registered mail, return receipt requested, in the United States mail, bearing
the address of such party as shown below. All such notices shall be deemed to
have been duly given as follows: at the time delivered by hand, if personally
delivered; three (3) business days after being deposited in the mail, postage
prepaid, if mailed; and on the next business day if timely delivered to an air
courier guaranteeing overnight delivery. The addresses for the purpose of this
paragraph 7 shall be those set forth below. These addresses may be changed by
giving written notice of such change in the manner provided in this Section 7
for giving notice.

          To Cone:

          Cone Mills Corporation
          1201 Maple Street
          Greensboro, North Carolina 27405
          Attn: President

          with copy to:

          Cone Mills Corporation
          1201 Maple Street
          Greensboro, North Carolina 27405
          Attn: General Counsel

          To LS&CO.:

          Levi Strauss & Co.
          Levi's Plaza
          1155 Battery Street/LS-7
          San Francisco,. California 94111
          Attn: President

                                       8
<PAGE>

          with copy to:

          Levi Strauss & Co.
          Levi's Plaza
          1155 Battery Street/LS-7
          San Francisco, California 94111
          Attn: General Counsel


          8.   Assignment; Binding Effect.  Neither Cone nor LS&CO. may assign
               --------------------------
its rights or delegate its duties without the written consent of the other
party, and any attempted assignment shall be void and unenforceable. This
Agreement shall be binding upon the successors (including, without limitation,
successors by merger, consolidation, sale of assets or otherwise by operation of
law) and permitted assigns of LS&CO. and Cone.

          9.   Entire Agreement: Amendment.  This Agreement, together with the
               ---------------------------
Order Documentation and the schedule of LS&CO.'s requirements in prior years for
XXX Denim previously prepared by the parties, contains all of the terms and
conditions agreed upon by Cone and LS&CO. relating to their subject matter, and
represents the final, complete and exclusive statement of the parties with
respect to that subject matter, and supersedes all prior agreements,
correspondence and communications (oral or written) with respect thereto between
the parties. If there is any inconsistency between this Agreement and any of the
order Documentation, this Agreement shall control. Neither this Agreement nor
the Order Documentation may be amended or modified except by an instrument in
writing signed by both parties.

          10.  Severability.  The provisions of this Agreement and the Order
               ------------
Documentation shall be applied and interpreted in a manner consistent with each
other so as to carry out the purposes and intent of the parties, but if for any
reason any of the provisions is unenforceable or invalid, such provision shall
be deemed severed from this Agreement or the Order Documentation, as the case
may be, and the remaining provisions shall be carried out with the same force
and effect as if the severed provision provisions had not been a part of this
Agreement or the Order Documentation, as the case may be.

          11.  Information About Control.  Cone shall promptly provide written
               -------------------------
notice to LS&CO. of the occurrence of any Change in Control and, in all events,
shall promptly provide LS&CO. with copies of: (i) all proxy statements,
registration statements, annual reports on Form 10-K, quarterly reports on Form
10-Q, current reports of Form 8-K and other documents it files with the
Securities and Exchange Commission and (ii) all statements on Schedules 13D, 13G
or 14D-1 under the Exchange Act, or notices under the Hart-Scott-Rodino
Antitrust Improvements Act of 1974, or acquiring person statements under The
North Carolina Control Share Acquisition Act, or

                                       9
<PAGE>

notices or statements called for by a "shareholder rights" or similar plan, it
receives from a third party.

          12.  Further Assurances.  Cone and LS&CO. agree to sign such other
               ------------------
documents (including, without limitation, the signing by Cone, after the
Applicable Change in Control and upon request of LS&CO., a memorandum of option,
for recording with the appropriate local real estate recorder), and to take such
other actions as may be appropriate in order to effect the transactions and
implement the relationships contemplated by this Agreement. For example, in view
of the importance to their relationship of management compatibility and
continuity, LS&CO. shall notify Cone of any changes in control of LS&CO., it
being understood that a change in control of LS&CO. does not affect in any way
either party's rights or obligations under this Agreement.

          13.  Remedial Matters.  It is expressly understood and agreed that the
               ----------------
provisions of this Agreement (including, without limitation, its Section 4) are
in addition to, and not in place or exclusive of, any rights and remedies Cone
or LS&CO. may have under applicable law, including those under the Uniform
Commercial Code or the common law. It is further understood and agreed that
damages would not adequately compensate LS&CO. were Cone to breach its
obligations to supply XXX Denim to LS&CO. under this Agreement, that XXX Denim
and the relationship of LS&CO. and Cone is unique and, therefore, that LS&CO.
shall be entitled to a decree of specific performance should Cone breach those
obligations.

          14.  Force Majeure.  Cone shall not be liable for any delay in its
               -------------
performance under this Agreement due to causes beyond its control, including,
without limitation, acts of God, riot, war, embargoes, acts of civil or military
authorities, fire, flood, inclement weather, accidents, quarantine restrictions,
strikes, delays in transportation, shortages of transportation, shortages of
material or labor or any other cause beyond its control.

          15.  Governing Law.  The validity, interpretation, and performance of
               -------------
this Agreement shall in all respects be governed by and construed according to
the laws of the state of California including, without limitation, Sections
2305(1)(b)(in respect of Section 2.2 of this Agreement) and 2306 (in respect of
Sections 2 and 3 of this Agreement) of, and the other provisions of, the
California Uniform Commercial Code.

          16.  Dispute Resolution.  Cone and LS&CO. agree that fast and
               ------------------
equitable Settlement of disputes arising under or in connection with this
Agreement is to their mutual advantage and is in the best interests of
maintaining the business relationships underlying this Agreement. To that end,
Cone and LS&CO. agree to use their best efforts (including, without limitation,
the participation of senior management) to resolve all differences of opinion
and to settle all disputes through cooperation and consultation.

                                       10
<PAGE>

          17.  Counterparts.  This Agreement may be signed in any number of
               ------------
counterparts, each of which shall be deemed an original but all of which
together shall constitute one and the same instrument.


          IN WITNESS WHEREOF, the parties have caused this Agreement to be
executed by their duly authorized officers as of the date and year first above
written.

                                                  CONE MILLS CORPORATION

                                                  By:  ________________________
                                                       Title: _________________


                                                  LEVI STRAUSS & CO.

                                                  By: _________________________
                                                      Title:___________________

Exhibits:

Exhibit A  Order Documentation
Exhibit B  Form of Lease Agreement

                                       11
<PAGE>

                      FIRST AMENDMENT TO SUPPLY AGREEMENT
                      -----------------------------------



          THIS IS A FIRST AMENDMENT TO SUPPLY AGREEMENT dated as of April 15,
1992 (the "First Amendment"), between CONE MILLS CORPORATION, a North Carolina
corporation ("Cone"), and LEVI STRAUSS & CO., a Delaware corporation ("LS&CO.").


                              B A C K G R O U N D
                              -------------------


          Cone and LS&CO. are parties to a Supply Agreement, dated as of March
30, 1992 (the "Agreement"). They wish to amend the Agreement in the manner
described in this First Amendment. This First Amendment is intended to be and is
an "instrument in writing signed by both parties" as contemplated by Section 9
(captioned "Entire Agreement; Amendment") of the Agreement.


THE PARTIES AGREE AS FOLLOWS:


1.   Amendment to Section 1 3
     ------------------------

          Section 1.3 of the Agreement is amended in its entirety as follows:

          "Order Documentation" means the purchase orders, confirmations of
          sales, invoices, releases, electronic data interchange protocols and
          communications and other documents and communications customarily used
          by Cone and LS&CO. in documenting orders by, and shipments to, LS&CO.,
          of XXX Denim.


2.   Amendment to Section 9
     ----------------------

          Section 9 of the Agreement is amending by amending its last sentence
in its entirety as follows:

          This Agreement may not be amended or modified except by an instrument
          in writing signed by both parties. The Order Documentation may not be
          amended or modified except as approved by both parties, it being
          understood that Cone and LS&CO. have and continue to work
          cooperatively in adapting new technologies and practices in order to
          improve the efficiency of ordering and shipment of XXX Denim.

                                       12
<PAGE>

3.   Conforming Changes
     ------------------

          The signature page of the Agreement is amended by deleting the phrase
"Exhibit A Order Documentation" appearing below the signatures, it being
understood that the Agreement now has only one exhibit, the form of lease
agreement identified as "Exhibit B."


4.   No Other Modifications
     ----------------------

          Except as expressly described in this First Amendment, Cone and LS&CO.
do not intend to and are not modifying any other provisions of the Agreement,
and the Agreement, as amended by this First Amendment, remains in full force and
effect


          IN WITNESS WHEREOF, the parties have caused this First Amendment to be
executed by their duly authorized officers as of the date and year first above
written.


                                                  CONE MILLS CORPORATION


                                                  By:  ________________________
                                                       Title: _________________



                                                  LEVI STRAUSS & CO.


                                                  By:  ________________________
                                                       Title: _________________

                                       13