Given a is an element of L(1)(R) and A the generator of an L(1)-integrable family of bounded and linear operators defined on a Banach space X, we prove the existence of an almost automorphic mild solution to the semilinear integral equation u(t) = integral(t)(-infinity) a(t - s)[Au(s) + f(s, u(s))]ds for each f : R x X -> X S(p)-almost automorphic in t, uniformly in x is an element of X, and satisfying diverse Lipschitz type conditions. For the scalar linear case, we prove that a is an element of L(1)(R) completely monotonic is already sufficient. (C) 2011 Elsevier Ltd. All rights reserved.