CHAPMAN AND CUTLER LLP                                   111 WEST MONROE STREET
                                                        CHICAGO, ILLINOIS 60603


                               December 2, 2013


Securities and Exchange Commission
100 F Street, N.E.
Washington, D.C. 20549


     Re:    First Trust Exchange-Traded AlphaDEX(R) Fund (the "Registrant")
                                 File No. 333-140895
            ---------------------------------------------------------------


Ladies and Gentlemen:

      On behalf of the Registrant, in accordance with the provisions of Rule
497(j) of Regulation C under the Securities Act of 1933, as amended, (the
"Securities Act"), this letter serves to certify that the most recent amendment
to the Registration Statement on Form N-1A (the "Registration Statement") of the
Registrant does not differ from that which would have been filed pursuant to
Rule 497(c) of the Securities Act. The Registration Statement relates to First
Trust Consumer Discretionary AlphaDEX(R) Fund, First Trust Consumer Staples
AlphaDEX(R) Fund, First Trust Energy AlphaDEX(R) Fund, First Trust Financials
AlphaDEX(R) Fund, First Trust Health Care AlphaDEX(R) Fund, First Trust
Industrials/Producer Durables AlphaDEX(R) Fund, First Trust Materials
AlphaDEX(R) Fund, First Trust Technology AlphaDEX(R) Fund, First Trust Utilities
AlphaDEX(R) Fund, First Trust Large Cap Core AlphaDEX(R) Fund, First Trust Mid
Cap Core AlphaDEX(R) Fund, First Trust Small Cap Core AlphaDEX(R) Fund, First
Trust Large Cap Value AlphaDEX(R) Fund, First Trust Large Cap Growth AlphaDEX(R)
Fund, First Trust Multi Cap Value AlphaDEX(R) Fund, First Trust Multi Cap Growth
AlphaDEX(R) Fund, First Trust Mid Cap Growth AlphaDEX(R) Fund, First Trust Mid
Cap Value AlphaDEX(R) Fund, First Trust Small Cap Growth AlphaDEX(R) Fund, First
Trust Small Cap Value AlphaDEX(R) Fund and First Trust Mega Cap AlphaDEX(R)
Fund, each a series of the Registrant. Post-Effective Amendment No. 21, which
was the most recent amendment to the Registration Statement, was filed
electronically with the Securities and Exchange Commission on November 22, 2012.

      If you have any questions or comments, please telephone the undersigned at
(312) 845-3484.

                                Very truly yours,

                                CHAPMAN AND CUTLER LLP



                                By: /s/ Morrison C. Warren
                                   ------------------------------------------
                                   Morrison C. Warren