Exhibit 4.34

Agreement

dated

March 31, 2016

between

Ocean Rig UDW Inc.

and

TMS Offshore Services Inc.

Whereas, Ocean Rig UDW Inc. (here after referred to as "OCR") is an international drilling contractor that owns and operates through its subsidiaries a fleet of ultra-deep water drilling units.

Whereas, TMS Offshore Services Inc. (here after referred to as "TMS") is a provider of management services in the offshore industry.

Whereas, OCR and TMS wish to record the main terms of their agreement, with any necessary management (or other) agreements to be entered into by OCR and/or any of its subsidiaries and TMS as required from time to time

Now therefore it is hereby agreed as follows:

1. OCR and its relevant subsidiaries will enter into one or more management agreements with TMS for the provision of certain management services associated with the management of its drilling units, including but not limited to:

a. Commercial Services

b. Financing Services

c. Legal Services

d. Manning Services

e. Catering Services

f. IT Services

g. Attendance Services

h. Insurance Services

i. Technical Services

j. Operations Services

2. Upon entering into the management agreements referred to above, OCR undertakes to terminate its respective agreements with Cardiff Drilling Inc.  ("CDI") and Vivid Finance Limited ("Vivid") with no compensation due by OCR, so that such services currently provided by CDI and Vivid are being provided solely by TMS as of the dates of the respective management agreements. In that regard, a reconciliation with any amounts paid to CDI and Vivid will be performed to keep OCR whole.

3. The financial terms for the provisions of the services shall be as follows:

a. A one-time setup fee of $2m payable on execution of the agreement

b. A monthly fee of $835,000 payable monthly in advance

c. Re-imbursement of all out-of-pocket expenses and travel expenses

d. A fee of 20bps on all financing transactions including but not limited to capital markets, debt and equity financings, waivers, interest rate swaps etc.

e. A fee of 100bps on all monies earned under any drilling contract

f. A fee of 75bps on all S&P and M&A transactions

g. A fee of $200 per person per day for offshore personnel provided through TMS

h. A fee of $100 per person per day for catering services provided through TMS

i. A fee of $2000 per person per day for superintendent attendance offshore provided by TMS

j. For Insurance, Technical and Operational services a separate fee schedule will be mutually  agreed once these services start being provided by TMS

4. The effective date for application of the above fee schedule will be January 1, 2016.

5. This agreement will be valid for a period of 10 years and OCR will have the right to terminate for convenience for a fee of $150m.

6. This agreement shall be governed and construed in accordance with English Law and any disputes arising hereunder shall be referred to arbitration in London, UK under the LMAA rules.

/s/Elpiniki Fotiou	/s/Dr. Adriano Cefai
For and on behalf of OCR	For and on behalf of TMS
Name:  Elpiniki Fotiou	Name:  Dr. Adriano Cefai
Title:    Senior Vice President of Finance and Accounting	Title:    Director of Mare Services Limited, Sole Director