CERTIFICATION FILED AS EXHIBIT 12(B) TO FORM N-CSR

Name of Issuer: AMG FUNDS III – AMG MANAGERS SPECIAL EQUITY FUND, AMG MANAGERS LOOMIS SAYLES BOND FUND, AND AMG MANAGERS GLOBAL INCOME OPPORTUNITY FUND

In connection with the Report on Form N-CSR of the above-named issuer that is accompanied by this certification, the undersigned hereby certifies, to his knowledge, that:

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

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the issuer.

Dated: September 6, 2017	/s/ Jeffrey T. Cerutti
	Jeffrey T. Cerutti
	Principal Executive Officer

CERTIFICATION FILED AS EXHIBIT 12(B) TO FORM N-CSR

Name of Issuer: AMG FUNDS III – AMG MANAGERS SPECIAL EQUITY FUND, AMG MANAGERS LOOMIS SAYLES BOND FUND, AND AMG MANAGERS GLOBAL INCOME OPPORTUNITY FUND

In connection with the Report on Form N-CSR of the above-named issuer that is accompanied by this certification, the undersigned hereby certifies, to his knowledge, that:

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

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the issuer.

Dated: September 6, 2017	/s/ Donald S. Rumery
	Donald S. Rumery
	Principal Financial Officer