In this paper the usual notions of superlinearity and sublinearity for semilinear problems like -Deltau =f (x, u) are given a local form and extended to indefinite nonlinearities. Here f (x, s) is allowed to change sign or to vanish for s near zero as well as for s near infinity. Some of the well-known results of Ambrosetti-Brezis-Cerami are partially extended to this context. (C) 2003 Elsevier Science (USA). All rights reserved.1992452467