CERTIFICATION PURSUANT TO RULE 30A-2(B) UNDER THE 1940 ACT AND SECTION 906
                           OF THE SARBANES-OXLEY ACT

I, James M. Dykas, President and Chief Executive Officer of First Trust Dynamic
Europe Equity Income Fund (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: February xx, 2016                 /s/ James M. Dykas
     -------------------                ----------------------------------------
                                        James M. Dykas, President and
                                        Chief Executive Officer
                                        (principal executive officer)


I, James M. Dykas, Treasurer, Chief Financial Officer and Chief Accounting
Officer of First Trust Dynamic Europe Equity Income Fund (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: February xx, 2016                 /s/ Donald P. Swade
     -------------------                ----------------------------------------
                                        Donald P. Swade, Treasurer,
                                        Chief Financial Officer and
                                        Chief Accounting Officer
                                        (principal financial officer)