Exhibit 99.1

AMENDMENT NO. 4

TO

STOCKHOLDERS RIGHTS AGREEMENT

This Amendment No. 4 (this “ Amendment ”) to the Stockholders Rights Agreement, made and entered into as of September 18, 2006, as amended by Amendment No. 1 thereto made and entered into as of August 6, 2010, Amendment No. 2 thereto made and entered into as of September 16, 2016 and Amendment No. 3 thereto made and entered into as of December 9, 2016 (the “ Rights Agreement ”), by and between Danaos Corporation, a Marshall Islands corporation (the “ Company ”), and American Stock Transfer & Trust Company, LLC, as Rights Agent (the “ Rights Agent ”), is made and entered into as of  December 15, 2017, by and between the Company and the Rights Agent.

WHEREAS, the parties hereto desire to amend the Rights Agreement on the terms and conditions contained herein.

NOW THEREFORE, in consideration of the premises and the mutual agreements set forth herein, the parties hereby agrees as follows:

1.              Certain Definitions .

(a) The definition of “ Final Expiration Date ” as set forth in Section 1 of the Rights Agreement is hereby deleted and replaced with the following:

“ Final Expiration Date ” shall mean December 17, 2018.

2.  Exhibit B — Form of Rights Certificate .

(a)  The first sentence of the introductory paragraph of Exhibit B of the Rights Agreement is hereby deleted and replaced with the following:

Not exercisable after December 17, 2018 or earlier if redemption or exchange occurs.

(b) The first sentence of the first paragraph following the introductory paragraphs of Exhibit B of the Rights Agreement is hereby deleted and replaced with the following:

This certificate certifies that                    , or registered assigns, is the registered owner of the number of Rights set forth above, each of which entitles the owner thereof, subject to the terms, provisions and conditions of the Stockholders Rights Agreement, dated as of September 18, 2006, as amended from time to time (the “Rights Agreement”), between Danaos Corporation, a Marshall Islands corporation (the “Company”), and American Stock Transfer & Trust Company, LLC (the “Rights Agent”), unless the Rights evidenced hereby have been previously redeemed by the

Company, to purchase from the Company at any time after the Distribution Date (as such term is defined in the Rights Agreement) and before 5:00 p.m., New York, New York time, on December 17, 2018 at the office of the Rights Agent, or at the office of its successor as Rights Agent, one one-thousandth (1/1000) of a fully paid, nonassessable share of Series A Participating Preferred Stock, $0.01 par value (the “Preferred Shares”), of the Company, at a purchase price of $25.00 per one one-thousandth (1/1000) of a Preferred Share (the “Purchase Price”), upon presentation and surrender of this Rights Certificate with the Form of Election to Purchase duly executed.

3. Exhibit C — Summary of Rights .

(a) The “Expiration of Rights” paragraph as set forth in Exhibit C of the Rights Agreement is hereby deleted and replaced with the following:

4.  No Further Amendments .  Except as expressly provided herein, the terms and conditions of the Rights Agreement shall continue in full force and effect.

5.  Counterparts .  This Amendment may be signed in counterparts, each of which shall be an original and all of which together shall constitute one and the same instrument.

6.  Governing Law .  This Amendment shall be governed by and construed in accordance with the laws of the State of New York, without giving effect to the conflicts of laws provisions thereof.

[Signature page follows.]

IN WITNESS WHEREOF, the parties have executed this Amendment as of the date first written above.