The authors prove the existence of an unstable manifold for solutions to the partial functional differential equation of the form u(t) = A(t)u(t) + f(t, u,), t attached R, under the conditions that the family of linear operators (A(t))' attached R generates the evolution family (U(t, s)ts) having an exponential dichotomy on the whole line R, and the nonlinear forcing term f satisfies the Fi-Lipschitz condition, i.e., ||f(t, Fi) - f(t, 1/1)|| or