Exhibit 99.1

AMENDMENT NO. 5

TO

STOCKHOLDERS RIGHTS AGREEMENT

This Amendment No. 5 (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, Amendment No. 3 thereto made and entered into as of December 9, 2016 and Amendment No. 4 made and entered into as of December 15, 2017 (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 July 9, 2018, 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 “ Acquiring Person ” as set forth in Section 1 of the Rights Agreement is hereby deleted and replaced with the following:

“ Acquiring Person ” shall mean any Person who or which, together with all Affiliates and Associates of such Person, shall be the Beneficial Owner of 23% or more of the shares of Common Stock then outstanding, but shall not include (i) the Company, (ii) any Subsidiary of the Company, (iii) any employee benefit plan of the Company or of any Subsidiary of the Company, or any entity holding shares of Common Stock for or pursuant to the terms of any such plan or (iv) an Exempted Person.  Notwithstanding the foregoing, no Person shall be deemed to be an Acquiring Person as the result of an acquisition of shares of Common Stock by the Company which, by reducing the number of shares outstanding, increases the proportionate number of shares beneficially owned by such Person to 23% or more of the shares of Common Stock of the Company then outstanding; provided, however, that a Person who (i) becomes the Beneficial Owner of 23% or more of the shares of Common Stock of the Company then outstanding by reason of share purchases by the Company and (ii) then after such share purchases by the Company, becomes the Beneficial Owner of any additional shares of Common Stock of the Company (other than pursuant to a dividend or distribution paid or made by the Company on the outstanding shares of Common Stock in shares of Common Stock or pursuant to a split or subdivision of the outstanding shares of Common Stock) representing one percent or more of the Common Stock then outstanding, such Person shall be deemed to be an Acquiring Person unless upon becoming the Beneficial Owner of such additional shares of Common Stock of the Company such Person does not beneficially own 23% or more of the shares of Common Stock of the Company then outstanding.  Notwithstanding the foregoing, (i) if the Company’s Board of Directors determines in good faith that a Person who would otherwise be an “Acquiring Person,” as defined herein, has become such inadvertently (including, without limitation, because (A) such Person was unaware that it beneficially owned a percentage of the shares of Common Stock that would otherwise cause such Person to be an “Acquiring Person,” as defined herein, or (B) such Person was aware of the extent of the shares of Common Stock it

beneficially owned but had no actual knowledge of the consequences of such beneficial ownership under this Agreement) and without any intention of changing or influencing control of the Company, and if such Person divested or divests as promptly as practicable a sufficient number of shares of Common Stock so that such Person would no longer be an “Acquiring Person,” as defined herein, then such Person shall not be deemed to be or to have become an “Acquiring Person” for any purposes of this Agreement; (ii) if, as of the date hereof, any Person is the Beneficial Owner of 23% or more of the shares of Common Stock outstanding, such Person shall not be or become an “Acquiring Person,” as defined herein, unless and until such time as such Person shall become the Beneficial Owner of additional shares of Common Stock (other than pursuant to a dividend or distribution paid or made by the Company on the outstanding shares of Common Stock in shares of Common Stock or pursuant to a split or subdivision of the outstanding shares of Common Stock), unless, upon becoming the Beneficial Owner of such additional shares of Common Stock, such Person is not then the Beneficial Owner of 23% or more of the shares of Common Stock then outstanding, or (iii) if a Person who would otherwise be an “Acquiring Person,” as defined herein, has become such as a result of acquiring shares of Common Stock from the Company in connection with the transactions contemplated by the Amended and Restated Restructuring Support Agreement, dated as of June 19, 2018, to which the Company is a party, including the “anti-dilution protection” rights contemplated thereby (the “ Anti-dilution Protection Rights ”), such Person shall not be or become an “Acquiring Person,” as defined herein, unless and until such time as such Person shall become the Beneficial Owner of additional shares of Common Stock (other than pursuant to (A) a dividend or distribution paid or made by the Company on the outstanding shares of Common Stock in shares of Common Stock, (B) a split or subdivision of the outstanding shares of Common Stock, (C) the exercise of warrants Beneficially Owned by such Person as of the date of such acquisition and (D) the Anti-dilution Protection Rights), unless, upon becoming the Beneficial Owner of such additional shares of Common Stock, such Person is not then the Beneficial Owner of 23% or more of the shares of Common Stock then outstanding;

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.