GLOBALSANTAFE CORPORATION (Company) Ordinary Shares TERMS AGREEMENT

Exhibit 10.2

GLOBALSANTAFE CORPORATION

(“Company”)

Ordinary Shares

TERMS AGREEMENT

April 14, 2005

Goldman, Sachs & Co.

As representative of the several

Underwriters named in Schedule I hereto

85 Broad Street

New York, NY 10004

Dear Sirs:

The undersigned agrees to sell to the several Underwriters named in Schedule I hereto for their respective accounts, and the Underwriters agree to purchase, severally and not jointly, on the terms and subject to the conditions of the Underwriting Agreement (“Underwriting Agreement”) attached hereto, the following securities (“Offered Securities”) on the following terms:

Title: Ordinary Shares, par value $0.01 per share, of GlobalSantaFe Corporation.

Aggregate Number of Shares: 23,500,000.

Purchase Price: $34.02 per share.

Expected Reoffering Price: $34.45 per share, subject to change by the underwriters.

Closing Date: April 20, 2005 at 10:00 a.m. (Eastern Daylight Time).

Place of Delivery and Payment: Baker Botts LLP; One Shell Plaza; 910 Louisiana Street, Houston, Texas 77002.

Method of and Specified Funds for Payment of Purchase Price: By wire transfer to a bank account specified by the Company in Federal (same day) funds.

Form/Method of Delivery of Offered Securities: Credit to Underwriters’ accounts at The Depository Trust Company.

1

Name and Address of Representative: Goldman, Sachs & Co. 85 Broad Street, New York, NY 10004.

Notice to Underwriters Shall Be Directed to: the Goldman, Sachs & Co. General Counsel (fax no.: (212) 902-9316) and confirmed to the General Counsel, at 85 Broad Street, New York, New York, 10004, Attention: General Counsel.

Counsel for the Underwriters: Andrews Kurth LLP.

Specified Subsidiaries: The Specified Subsidiaries are set forth on Schedule II hereto.

Over-allotment Provisions: None

Lock-up Period (if any): With respect to the Company, for a period of 90 days from the date of the Terms Agreement.

The respective number of shares of the Offered Securities to be purchased by each of the Underwriters are set forth opposite their names in Schedule I hereto.

The provisions of the Underwriting Agreement are incorporated herein by reference and are deemed to be a part hereof, subject to any changes or amendments to the Underwriting Agreement as set forth above.

2

If the foregoing is in accordance with your understanding of our agreement, kindly sign and return to the Company one of the counterparts hereof, whereupon it will become a binding agreement between the Company and the several Underwriters in accordance with its terms.

3

The foregoing Terms Agreement is hereby

confirmed and accepted as of the date first above

written.

Goldman, Sachs & Co.

J.P. Morgan Securities Inc.

Citigroup Global Markets Inc.

Credit Suisse First Boston LLC

4

SCHEDULE I

5

SCHEDULE II

Specified Subsidiaries

Global Marine Inc.

GlobalSantaFe Drilling Company

Applied Drilling Technology Inc.

Challenger Minerals Inc.

GlobalSantaFe Drilling Operations Inc.

GlobalSantaFe International Services Inc.

GlobalSantaFe International Drilling Corporation

GlobalSantaFe International Drilling Inc.

GlobalSantaFe Operations (BVI) Inc.

GlobalSantaFe South America LLC

GlobalSantaFe Hungary Services Limited Liability Company

GlobalSantaFe Drilling U.K. Limited

6