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                                                                 Exhibit 31.1

                                CERTIFICATION
                                -------------

I, Zsolt Rumy, certify that:

         (1)      I have reviewed this quarterly report on Form 10-Q of
                  Zoltek Companies, Inc.;

         (2)      Based on my knowledge, this quarterly report does not
                  contain any untrue statement of a material fact or omit to
                  state a material fact necessary in order 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 quarterly report;

         (3)      Based on my knowledge, the financial statements, and other
                  financial information included in this quarterly 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
                  quarterly 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-14 and 15d-14) 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 for which this quarterly report is being
                           prepared;

                  (b)      evaluated the effectiveness of the registrant's
                           disclosure controls and procedures and presented
                           in this report our conclusions about the
                           effectiveness of the disclosure controls and
                           procedures, as of the end of the period covered
                           by this quarterly report based on such
                           evaluation; and

                  (c)      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 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 the 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 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
                           controls over financial report.

February 9, 2005                 /s/ ZSOLT RUMY
                                 -----------------------
                                 Zsolt Rumy
                                 Chief Executive Officer