AbstractWe obtain a C1 center manifold theorem for perturbations of delay difference equations in Banach spaces with infinite delay. Our results extend in several directions the existing center manifold theorems. Besides considering infinite delay equations, we consider perturbations of nonuniform exponential trichotomies and generalized trichotomies that may exhibit stable, unstable and central behaviors with respect to arbitrary asymptotic rates ecρ(n) for some diverging sequence ρ(n). This includes as a very special case the usual exponential behavior with ρ(n)=n.