EXHIBIT (b)


         Certification Pursuant to Rule 30a-2(b) under the 1940 Act and


                      Section 906 of the Sarbanes-Oxley Act


I, James A. Bowen, Chairman of the Board, President and Chief Executive Officer
of First Trust Exchange-Traded AlphaDEX(TM) 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:  September 24, 2007
      ---------------------------

                                          /s/ James A. Bowen
                                          -------------------------------------
                                          James A. Bowen, Chairman of the Board,
                                          President and Chief Executive Officer
                                          (principal executive officer)



I, Mark R. Bradley, Treasurer, Controller, Chief Financial Officer and Chief
Accounting Officer of First Trust Exchange-Traded AlphaDEX(TM) 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:  September 24, 2007
      ----------------------

                                         /s/ Mark R. Bradley
                                         -------------------------------------
                                         Mark R. Bradley Treasurer, Controller,
                                         Chief Financial Officer and
                                         Chief Accounting Officer
                                         (principal financial officer)