# EXHIBIT 31.1

# CERTIFICATION OF CHIEF
EXECUTIVE OFFICER PURSUANT TO

# SECTION 302 OF THE
SARBANES-OXLEY ACT OF 2002

I, Krish Prabhu, certify
that:

| | 1. | I have reviewed this quarterly report on Form 10-Q of Tellabs, Inc.;
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| | 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;
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| | 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;
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| | 4. | The registrant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)) for the registrant and have:
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| |  | 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;
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| |  | 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 report based on such evaluation; and
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| |  | 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
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| | 5. | The registrants other certifying officers 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:
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| |  | 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 registrants ability to record, process, summarize and
          report financial information; and
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| |  | 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.
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Dated: August 10, 2004

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| |  | -----------------------
| |  | /s/ Krish Prabhu       
| |  | Krish Prabhu           
| |  | Chief Executive Officer