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                                                                 EXHIBIT 31.1

                     CERTIFICATIONS PURSUANT TO SECTION 302
                        OF THE SARBANES-OXLEY ACT OF 2002

I, Edward J. Marino, Chief Executive Officer and President of Presstek, Inc.
certify that:

     1. I have reviewed this report on Form 10-K of Presstek, Inc.;

     2. Based on my knowledge, this 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 report;

     3. Based on my knowledge, the financial statements, and other financial
information included in this report, fairly present in all material respects the
financial condition, results of operations and cash flows of the registrant as
of, and for, the periods presented in this report;

     4. The registrant's other certifying officer 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
registrant 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 registrant, including its
consolidated subsidiaries, is made known to us by others within those entities,
particularly during the period in which this 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 registrant's disclosure controls
and procedures, and presented in this report our conclusions about the
effectiveness of the disclosures controls and procedures, as of the end of the
period covered by this report based on such evaluation; and

        d) disclosed in this report any change in the registrant's internal
control over financial reporting that occurred during the registrant's most
recent fiscal quarter (the registrant's fourth fiscal quarter in the case of an
Annual Report) that has materially affected, or is reasonably likely to
materially affect, the registrant's internal control over financial reporting;
and

     5. The registrant's other certifying officer and I have disclosed, based on
our most recent evaluation of internal control over financial reporting, to the
registrant's auditors and the audit committee of registrant's board of directors
(or persons performing the equivalent function):

        a) all significant deficiencies and material weaknesses in the design or
operation of internal controls over financial reporting which are reasonably
likely to adversely affect the registrant'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 registrant's internal control over
financial reporting.


                                        /s/ Edward J. Marino
                                        --------------------
                                        Edward J. Marino
                                        Chief Executive Officer and President
                                        (Principal Executive Officer)

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March 17, 2005