This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form−div (a(x, x/εh, Duh)) =fhon Ω with Dirichlet boundary conditions. The sequence (εh) tends to 0 and the mapa(x, y, ξ) is periodic iny, monotone inξand satisfies suitable continuity conditions. It is proved thatuh→ uweakly inwhereuis the solution of a homogenized problem−div(b(x, Du)) =fon Ω. We also prove some corrector results, i.e. we find (Ph) such thatDuh− Ph(Du)→0 inL2(Ω, Rn).