BNY Mellon Investment Funds III N-CSRS Certified semi-annual shareholder report (management investment company)

[EX-99.906CERT]

Exhibit (b)

SECTION 906 CERTIFICATIONS

            In connection with this report on Form N-CSR for the Registrant as furnished to the Securities and Exchange Commission on the date hereof (the "Report"), the undersigned hereby certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

            (1)        the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as applicable; and

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

By: /s/ Bradley J. Skapyak

Bradley J. Skapyak,

           President

Date: June 17, 2013

By: /s/ James Windels

      James Windels,

      Treasurer

Date: June 17, 2013

This certificate is furnished pursuant to the requirements of Form N-CSR and shall not be deemed "filed" for purposes of Section 18 of the Securities Exchange Act of 1934, or otherwise subject to the liability of that section, and shall not be deemed to be incorporated by reference into any filing under the Securities Act of 1933 or the Securities Exchange Act of 1934.