In this paper we study the problem -Delta(p)u = f(x, u, del u) in Omega u = 0 on partial derivative Omega, where Omega subset of R-N is a smooth bounded domain, N greater than or equal to 2, and Delta(p)u = div(\del u\(p-2) del u) defines the p-Laplacian. We provide some necessary and sufficient conditions on f under which the problem admits a weak solution. For the case p = 2 we obtain more general conditions on f. The main ingredients are degree theory and the super-subsolution method. (C) 2000 Academic Press.2452303316