Let N >= 1, 1 < p < infinity and p* = max(1,p - 1).; 1_. Let W be a bounded domain of R-N. We establish the strong maximum principle for the p-Laplace operator with a nonlinear potential term. More precisely, we show that every super-solution u is an element of W-loc(1,p*) (Omega) vanishes identically in Omega, if u is admissible and u = 0 a.e on a set of positive p-capacity relative to Omega.