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In this paper we study quasilinear elliptic systems with nonlinear boundarycondition with fully coupled perturbations even on the boundary. Under verygeneral assumptions our main result says that each weak solution of suchsystems belongs to $L^\infty(\close)\times L^\infty(\close)$. The proof isbased on Moser's iteration scheme. The results presented here can also beapplied to elliptic systems with homogeneous Dirichlet boundary condition.

Global a priori bounds for weak solutions of quasilinear elliptic systems with nonlinear boundary condition