President

Section 906 Certification under Sarbanes Oxley Act

I, Brian E. Binder, certify that:

1.   I have reviewed this report, filed on behalf of Deutsche Multi-Market Income Trust, on Form N-CSRS;

2.   Based on my knowledge and pursuant to 18 U.S.C. § 1350, the periodic report on Form N-CSRS (the “Report”) fully complies with the requirements of § 13 (a) or § 15 (d), as applicable, of the Securities Exchange Act of 1934 and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

July 30, 2015	/s/Brian E. Binder
	Brian E. Binder
	President

Chief Financial Officer and Treasurer

Section 906 Certification under Sarbanes Oxley Act

I, Paul Schubert, certify that:

1.   I have reviewed this report, filed on behalf of Deutsche Multi-Market Income Trust, on Form N-CSRS;

2.   Based on my knowledge and pursuant to 18 U.S.C. § 1350, the periodic report on Form N-CSRS (the “Report”) fully complies with the requirements of § 13 (a) or § 15 (d), as applicable, of the Securities Exchange Act of 1934 and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

July 30, 2015	/s/Paul Schubert
	Paul Schubert
	Chief Financial Officer and Treasurer