Certification Pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of
the Sarbanes-Oxley Act of 2002; provided by the Chief Executive Officer and
Chief Financial Officer, based on each such officer's knowledge and belief.

The undersigned officers of Nuveen Tax-Advantaged Total Return Strategy Fund
(the "Fund"), certify that, to the best of each such officer's knowledge and
belief:

      1.    The Form N-CSR of the Fund for the period ended June 30, 2006 (the
            "Report") fully complies with the requirements of Section 13(a) or
            15(d) of the Securities Exchange Act of 1934; and

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

Date: September 8, 2006

                                          /s/ Gifford R. Zimmerman
                                          ---------------------------------
                                          Gifford R. Zimmerman
                                          Chief Administrative Officer
                                          (principal executive officer)

                                          /s/ Stephen D. Foy
                                          ---------------------------------
                                          Stephen D. Foy
                                          Vice President, Controller
                                          (principal financial officer)