Exhibit 12.1  CERTIFICATIONS  I,
Dr. John Coustas, certify that:  1.I have reviewed this annual
report on Form 20-F of Danaos Corporation;  2.Based on my knowledge, this
annual report does not contain any untrue statement of a material fact or omit
to state a material fact necessary to make the statements made, in light of the
circumstances under which such statements were made, not misleading with
respect to the period covered by this annual report;  3.Based on my knowledge, the
financial statements, and other financial information included in this annual
report, fairly present in all material respects the financial condition,
results of operations and cash flows of the company as of, and for, the periods
presented in this annual report;  4.The Companys other
certifying officers and I are responsible for establishing and maintaining
disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and
15d-15(e)) and internal control over financial reporting (as defined in
Exchange Act Rules 13a-15(f) and 15d-15(f)) for the Company and have;  a.)designed such disclosure
controls and procedures, or caused such disclosure controls and procedures to
be designed under our supervision, to ensure that material information relating
to the company, including its consolidated subsidiaries, is made known to us by
others within those entities, particularly during the period in which this
annual report is being prepared;  b.)designed such internal
control over financial reporting, or caused such internal control over
financial reporting to be designed under our supervision, to provide reasonable
assurance regarding the reliability of financial reporting and the preparation
of financial statements for external purposes in accordance with generally
accepted accounting principles;  c.)evaluated the effectiveness
of the Companys disclosure controls and procedures and resented in this annual
report our conclusions about the effectiveness of the disclosure controls and
procedures, as of the end of the period covered by this report based on such
evaluation; and  d.)disclosed in this annual
report any change in the Companys internal control over financial reporting
that occurred during the period covered by the annual report that has
materially affected, or is reasonably likely to materially affect, the Companys
internal control over financial reporting; and  5.The Companys other
certifying officers and I have disclosed, based on our most recent evaluation
of internal control over financial reporting, to the Companys auditors and the
audit committee of theCompanys board of directors (or persons performing the
equivalent function):  a.)all significant deficiencies
and material weaknesses in the design or operation of internal control over
financial reporting which are reasonably likely to adversely affect the Companys
ability to record, process, summarize and report financial information; and  b.)any fraud, whether or not
material, that involves management or other employees who have a significant
role in the Companys internal control over financial reporting.  Date:
June 18, 2010  /s/
  Dr. John CoustasDr. John
  CoustasPresident
  and Chief Executive Officer