Certification Pursuant to Rule 30a-2(b) under the 1940 Act and Section 906 of the Sarbanes-Oxley Act

I, Nicholas Dalmaso, Chief Executive Officer of Destra Investment Trust II (the “Registrant”), certify that:

1. The Form N-CSR of the Registrant (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

Date:                      May 27, 2014     /s/ Nicholas Dalmaso

Nicholas Dalmaso, Chief Executive Officer

(principal executive officer)

I, Linda Fryer, Chief Financial Officer of Destra Investment Trust II (the “Registrant”), certify that:

1. The Form N-CSR of the Registrant (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

Date:                      May 27, 2014     /s/ Linda Fryer

Linda Fryer, Chief Financial Officer

(principal financial officer)