EXHIBIT 10.1

AMENDMENT NO.1 TO
MAY PURCHASE AGREEMENT

     THIS AMENDMENT NO.1 to May Purchase Agreement (this “Amendment”), dated as
of November 4, 2004, to the Purchase Agreement, dated as of May 27, 2004 (the
“Purchase Agreement”), is made and entered into by and among HORIZON OFFSHORE,
INC., a Delaware corporation (the “Issuer”), the Guarantors listed on the
signature pages hereof (the “Guarantors” together with the Issuer, the
“Obligors”) and the Noteholders listed on the signature pages hereof (“New
Additional Noteholders”).

W I T N E S S E T H:

     WHEREAS, the Obligors and the Noteholders listed on the signature pages
hereof desire to amend certain provisions of the Purchase Agreement, as more
particularly set forth below, in order to permit the issuance by the Issuer of
$9,625,000 aggregate principal amount of its 18% Subordinated Secured Notes due
March 31, 2007, for an aggregate purchase price of $7,700,000 (the “New
Additional Notes”) pursuant to the Purchase Agreement as amended hereby;

     WHEREAS, the parties hereto agree that such New Additional Notes shall be
classified as Additional Notes under the Purchase Agreement, as amended hereby;
and

     WHEREAS, such amendment requires the approval of the Required Holders.

     NOW THEREFORE, in consideration of the foregoing, the parties hereto agree
as follows:

     1. Definitions. Except as otherwise provided in this Amendment, capitalized
terms used in this Amendment shall have the meanings set forth for such terms in
the Purchase Agreement.

     2. Effectiveness. This Amendment shall be effective upon the execution
hereof by the Obligors and the Required Holders.

     3. Representation and Warranty of each New Additional Noteholder. Each New
Additional Noteholder represents and warrants that it is currently the holder as
of the date hereof of the aggregate principal amount of the Notes set forth
under its name on the signature pages hereof.

     4. Due Authorization. Each Obligor represents and warrants that the
execution and delivery by it of this Amendment and of each other Document
executed or to be executed by it has been duly authorized by all necessary
corporate action, does not require any Approval (except those Approvals already
obtained), does not and will not conflict with, result in any violation of, or
constitute any default under, any provision of any Organic Document or
Contractual Obligation of such Obligor or any law or governmental regulation or
court decree or order, and will not result in or require the creation or
imposition of any Lien on the properties of such Obligor pursuant to the
provisions of any Contractual Obligation of such Obligor, except for Liens
imposed pursuant to this Amendment, the Purchase Agreement or any other
Document.

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     5. Validity, etc. Each Obligor represents and warrants that this Amendment
constitutes the legal, valid and binding obligation of such Obligor, enforceable
in accordance with its terms subject, as to enforcement of remedies, to
bankruptcy, insolvency, reorganization, moratorium, or similar laws affecting
rights of creditors generally and to the effect of general principles of equity.

     6. Amendment of Recital A. Recital A of the Purchase Agreement is hereby
amended and restated in its entirety as follows:

     A. The Issuer desires to issue (1) $18,750,000 aggregate principal amount
of its 18% Subordinated Secured Notes due March 31, 2007 and (2) up to an
additional $14,916,685 aggregate principal amount of its 18% Subordinated
Secured Notes due March 31, 2007 at the option of the Noteholders in accordance
with Section 2.4(b) hereof; and

     7. Amendment of Section 1.2. Section 1.2 of the Purchase Agreement is
hereby amended to add the following language as sub-paragraph (b) thereunder:

     (b) Subject to the terms and conditions of the Purchase Agreement, as
amended hereby, the Issuer will issue and sell to the Noteholders, and the
Noteholders, acting severally and not jointly, agree to purchase the New
Additional Notes in the respective amounts set forth in Exhibit A attached
hereto, at the purchase price set forth therein (the “Purchase Price”). The sale
and purchase of such New Additional Notes (the “Closing”) will occur at the
offices of Akin Gump Strauss Hauer & Feld, LLP, 1111 Louisiana, 44th Floor,
Houston, Texas 77002 at 10:00 a.m., on November 4, 2004 (the “Closing Date”). At
the Closing, the Issuer shall deliver such New Additional Notes to the
Noteholders in such denominations as the Noteholders shall request, dated as of
the Closing Date, against delivery by the Noteholders to the Issuer of
immediately available funds in the amount of the Purchase Price by wire transfer
to the account of Horizon Offshore Contractors, Inc., account number 159506 at
Southwest Bank of Texas, N.A., Houston, Texas, ABA No. 113011258. If the Issuer
shall fail to tender such New Additional Notes to the Noteholders as provided in
this Paragraph 8, or any of the conditions specified in Article 4 of the
Purchase Agreement shall have not been fulfilled to the satisfaction of the
Noteholders, the Noteholders shall have no obligations under this Amendment,
without waiving any rights they may have by reason of such failure or such
nonfulfillment.

     8. Amendment of Section 2.4(b). Section 2.4(b) of the Purchase Agreement is
hereby amended and restated in its entirety as follows:

     (b) The Noteholders shall have the option, but not the obligation, to
purchase from time to time up to $11,933,348 aggregate purchase price of
Additional Notes in accordance with the procedures set forth below. In the event
that any or all of the Noteholders elect to purchase Additional Notes pursuant
to the immediately preceding sentence, the Issuer agrees to issue such
Additional Notes on the same terms and conditions set forth in this Agreement.
If any

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Noteholder elects to purchase Additional Notes pursuant to this Section 2.4(b),
such Noteholder shall give notice of such election and the aggregate purchase
price of such intended purchase to the Issuer and the other Noteholders and
shall give such other Noteholders an opportunity to purchase Additional Notes
pursuant to this Section 2.4(b). In the event that the aggregate purchase price
of Additional Notes that all of the Noteholders intend to purchase exceeds
$11,933,348, then the amount of Additional Notes to be issued and sold to each
Noteholder shall be reduced on as nearly a pro rata basis as practicable.

     9. Amendment to Section 6.1.14. Section 6.1.14 of the Purchase Agreement is
hereby amended to add the following language as sub-paragraph (b) thereunder:

     (b) Neither the Issuer nor any Subsidiary shall amend any Indebtedness
document of any kind whatsoever without the consent of the Required Holders;
provided that neither the Issuer nor any Subsidiary shall be required to obtain
the consent of the Required Holders with respect to amendments to Indebtedness
documents to which the CIT Group/Equipment Financing, Inc. is a party.

     10. Ratification of Purchase Agreement. The parties hereto hereby ratify
and confirm all of the terms and conditions of the Purchase Agreement, as
amended hereby, and except as modified, amended or supplemented by this
Amendment, all of the terms and provisions of the Purchase Agreement shall
remain in full force and effect.

     11. Waivers. Each of the New Additional Noteholders hereby consents to the
issuance of the New Additional Notes and all of the other transactions
contemplated by this Amendment, including, without limitation, the taking of any
action with respect to collateral and the issuance of additional New Additional
Notes, and in furtherance thereof hereby waive compliance with all of the
provisions contained in the Purchase Agreement and the other Documents to the
fullest extent necessary to permit the execution and delivery of this Agreement,
the issuance of the New Additional Notes and all of the other transactions
contemplated by this Agreement.

     12. Required Noteholders. The Obligors and the New Additional Noteholders
acknowledge and agree that such New Additional Noteholders represent the
“Required Noteholders” as defined in the Purchase Agreement.

     13. Counterparts; Effectiveness. This Amendment may be executed by the
parties hereto in several counterparts, each of which shall be deemed to be an
original and all of which shall constitute together but one and the same
agreement. This Amendment shall become effective when counterparts hereof have
been executed by the Issuer and each Noteholder listed on the signature pages
hereof.

     14. Headings. The various headings of this Amendment are inserted for
convenience only and shall not affect the meanings or interpretation of this
Amendment or any provisions hereof.

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

            ISSUER:

HORIZON OFFSHORE, INC.
      By:   /s/ David W. Sharp       Name:  David W. Sharp      
Title:    Executive Vice President    

[Amendment to May Purchase Agreement]

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            GUARANTORS:

HORIZON VESSELS, INC.
      By:   /s/ David W. Sharp       Name:  David W. Sharp      
Title:    Executive Vice President    

[Amendment to May Purchase Agreement]

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            HORIZON OFFSHORE CONTRACTORS, INC.
      By:   /s/ David W. Sharp       Name:  David W. Sharp      
Title:    Executive Vice President    

[Amendment to May Purchase Agreement]

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            HORIZON SUBSEA SERVICES, INC.
      By:   /s/ David W. Sharp       Name:  David W. Sharp      
Title:    Executive Vice President    

[Amendment to May Purchase Agreement]

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            HORIZON VESSELS INTERNATIONAL, LTD.
      By:   /s/ David W. Sharp       Name:  David W. Sharp      
Title:    Executive Vice President    

[Amendment to May Purchase Agreement]

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            HorizEN, LLC
      By:   /s/ David W. Sharp       Name:  David W. Sharp      
Title:    Executive Vice President    

[Amendment to May Purchase Agreement]

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            ECH OFFSHORE, S. de R.L. de C.V.
      By:   /s/ Bill J. Lam       Name:  Bill J. Lam       Title:    Sole
Manager    

[Amendment to May Purchase Agreement]

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            HOC OFFSHORE, S. de R.L. de C.V.
      By:   /s/ Bill J. Lann       Name:  Bill J. Lann       Title:    President
   

[Amendment to May Purchase Agreement]

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                  NEW ADDITIONAL NOTEHOLDERS:
 
                ELLIOTT ASSOCIATES, L.P.
 
                By:   Elliott Capital Advisors, L.P.,         as General Partner
 
                By:   Braxton Associates, Inc.,         as General Partner
 
           

  By:   /s/ Elliot Greenberg        

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      Name:   Elliot Greenberg

      Title:   Vice President
 
                Aggregate Principal Amount: $2,384,284.08
 
                Address:   712 Fifth Avenue

          36th Floor

          New York, New York 10019
 
                ELLIOTT INTERNATIONAL, L.P.
 
                By:   Elliott International Capital Advisors Inc.,         as
Attorney-in-Fact
 
           

  By:   /s/ Elliot Greenberg        

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      Name:   Elliot Greenberg

      Title:   Vice President
 
                Aggregate Principal Amount: $3,576,426.10
 
                Address:   712 Fifth Avenue

          36th Floor

          New York, New York 10019

[Amendment to May Purchase Agreement]

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                  FALCON MEZZANINE PARTNERS, LP
 
                By:   Falcon Mezzanine Investments, LLC, its         General
Partner
 
           

  By:   /s/ Eric Y. Rogoff        

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      Name:   Eric Y. Rogoff

      Title:   Vice President
 
                Aggregate Principal Amount: $5,259,450.45
 
                Address:   60 Kendrick Street

          Needham, Massachusetts 02494
 
                Telecopier No.: (781) 247-7299

[Amendment to May Purchase Agreement]

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                  B. RILEY & CO., INC.
 
           

  By:   /s/ Bryant Riley        

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      Name:   Bryant Riley

      Title:   Chairman
 
                Aggregate Principal Amount: $210,378.42
 
                Address:   11100 Santa Monica Blvd., Suite 800

          Los Angeles, CA 90025

[Amendment to May Purchase Agreement]

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                  SACC PARTNERS, LP
 
           

  By:   /s/ Tom Kelleher        

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      Name:   Tom Kelleher

      Title:   General Partner
 
                Aggregate Principal Amount: $2,384,284.06
 
                Address:   11100 Santa Monica Blvd., Suite 800

          Los Angeles, CA 90025

[Amendment to May Purchase Agreement]

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                  LLOYD I. MILLER
 
           

  By:   /s/ Lloyd I. Miller        

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      Name:   Lloyd I. Miller

      in his individual capacity
 
                Aggregate Principal Amount: $2,699,851.69
 
                Address:   4550 Gordon Drive

          Naples, FL 34102

[Amendment to May Purchase Agreement]

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                  MILFAM I, L.P.
 
           

  By:   /s/ Lloyd I. Miller        

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      Name:   Lloyd I. Miller

      Title:   Limited Partner
 
                Aggregate Principal Amount: $2,699,851.69
 
                Address:   4550 Gordon Drive

          Naples, FL 34102

[Amendment to May Purchase Agreement]

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EXHIBIT A

NEW ADDITIONAL NOTES PURCHASED BY INVESTORS

                      Principal Amount of         Notes to be     Purchaser

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  Purchased

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  Purchase Price

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Elliott Associates, L.P.
  $ 1,324,500     $ 1,059,600  
Elliott International, L.P.
  $ 1,986,750     $ 1,589,400  
Falcon Mezzanine Partners, LP
  $ 1,875,000     $ 1,500,000  
B. Riley & Co., Inc.
  $ 116,250     $ 93,000  
SACC Partners, LP
  $ 1,323,750     $ 1,059,000  
Lloyd I. Miller
  $ 1,499,375     $ 1,199,500  
MilFam I, L.P.
  $ 1,499,375     $ 1,199,500  
 
   

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Total:
  $ 9,625,000     $ 7,700,000  
 
   

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A-1