We consider weak solutions u ∈ u0 +W 1,2 0 (Ω,R )∩L∞(Ω,RN ) of second order nonlinear elliptic systems of the type −div a( · , u,Du) = b( · , u,Du) in Ω with an inhomogeneity obeying a natural growth condition. In dimensions n ∈ {2, 3, 4} we show that Hn−1-almost every boundary point is a regular point for Du, provided that the boundary data and the coefficients are sufficiently smooth. Mathema...