  We consider weak solutions $u \in u_0 + W^{1,2}_0(\Omega,R^N) \cap
L^{\infty}(\Omega,R^N)$ of second order nonlinear elliptic systems of the type
$- div a (\cdot, u, Du) = b(\cdot,u,Du)$ in $\Omega$ with an inhomogeneity
satisfying a natural growth condition. In dimensions $n \in \{2,3,4\}$ we show
that $\mathcal{H}^{n-1}$-almost every boundary point is a regular point for
$Du$, provided that the boundary data and the coefficients are sufficiently
smooth.
