**Exhibit 31.1**CERTIFICATION OF CHIEF EXECUTIVE OFFICERI, Lukas Braunschweiler, certify that:1. I have reviewed this Annual Report on Form 10-K of Dionex Corporation; 2. Based on my knowledge, this report does not contain any untrue statement of a material fact oromit to state a material fact necessary to make the statements made, in light of the circumstances under whichsuch 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 inthis report, fairly present in all material respects the financial condition, results of operations and cash flowsof the registrant as of, and for, the periods presented in this report; 4. The registrant’s other certifying officer(s) and I are responsible for establishing andmaintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internalcontrol over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) forthe registrant and have: (a) Designed such disclosure controls and procedures, or caused such disclosure controls andprocedures to be designed under our supervision, to ensure that material information relating to theregistrant, 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 controlover financial reporting to be designed under our supervision, to provide reasonableassurance regarding the reliability of financial reporting and the preparation of financialstatements for external purposes in accordance with generally accepted accountingprinciples;  (c) Evaluated the effectiveness of the registrant’s disclosure controls and procedures andpresented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of theend 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 financialreporting that occurred during the registrant’s most recent fiscal quarter (the registrant’s fourth fiscal quarter inthe case of an annual report) that has materially affected, or is reasonably likely to materially effect, theregistrant’s internal control over financial reporting; and5. The registrant’s other certifying officer(s) and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the registrant’s auditors and the audit committee ofregistrant’s board of directors (or persons performing the equivalent functions): (a) All significant deficiencies and material weaknesses in the design or operation ofinternal control over financial reporting which are reasonably likely to adversely affect the registrant’s abilityto record, process, summarize and report financial information; and  (b) Any fraud, whether or not material, that involves management or other employees who havea significant role in the registrant’s internal control over financial reporting.Date: October 12, 2005        /s/ Lukas Braunschweiler  Lukas Braunschweiler  President, Chief Executive Officer and Director