Abstract: By means of the methods presented in the topological degree theory, the existence of periodic solutions to a type of the Duffing functional differential equation x''(t)+g(x(t - τ(t, x(t))))=f(t) with complex time lag is studied, sufficient and necessary condition of the equation with periodic solutions is obtained, and the existence and uniqueness of periodic solutions is given when the time lag is constant, the instance is given to the problem.

Key words: Time lag, Duffing equation, Periodic solutions, Degree