Exhibit 32.1

Certification of Chief Executive Officer

Pursuant to 18 U.S.C. § 1350, as created by Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned officer of ResMed Inc, a Delaware corporation (the “Company”), hereby certifies, to his knowledge, that:

(i) the accompanying Quarterly Report on Form 10-Q of the Company for the period ended December 31, 2005 (the “Report”) fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(ii) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

February 7, 2006

/s/    PETER C. FARRELL        

Peter C. Farrell

Chairman and Chief Executive Officer

A signed original of this written statement required by Section 906 has been provided to ResMed Inc and will be retained by ResMed Inc and furnished to the Securities and Exchange Commission or its staff upon request.

Certification of Chief Financial Officer

Pursuant to 18 U.S.C. § 1350, as created by Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned officer of ResMed Inc, a Delaware corporation (the “Company”), hereby certifies, to his knowledge, that:

(i) the accompanying Quarterly Report on Form 10-Q of the Company for the period ended December 31, 2005 (the “Report”) fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(ii) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

February 7, 2006

/s/    BRETT A. SANDERCOCK        

Brett A. Sandercock

Vice President Finance and Chief Financial Officer

A signed original of this written statement required by Section 906 has been provided to ResMed Inc and will be retained by ResMed Inc and furnished to the Securities and Exchange Commission or its staff upon request.