In this work, we consider an elliptic system of two equations in dimension one (with Neumann boundary conditions) where the nonlinearities are asymptotically linear at -infinity and superlinear at +infinity. We obtain that, under suitable hypotheses, a solution exists for any couple of forcing terms in L-2. We also present a similar result in which the superlinearity is in only one of the two equations, and we discuss the resonant problem too. (c) 2005 Elsevier Inc. All rights reserved.3221403419