In this paper, we extend Bourgain's double recurrence result to the Wiener-Wintner averages. Let in the work of B. Host and B. Kra [14] (these characteristic factors were also developed independently by T. Ziegler [20] without the use of seminorms).Definition 2.1. Let (X, F , µ, T) be an ergodic dynamical system on a probability measure space. The factors Z k are defined in terms of seminorms as follows.• The factor Z 0 is the trivial σ-algebra.• The factor Z 1 can be characterized by the seminorm |||·||| 2 where ||| f ||| 4 2 = lim H→∞

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