  Let $\Omega$ and $\widetilde{\Omega}$ be domains in the Euclidean space
$\mathbb R^n$. We study the boundary behavior of weak $(p,q)$-quasiconformal
mappings, $\varphi:\Omega\to \widetilde{\Omega}$, $n-1<q\leq p<n$. The
suggested method is based on the capacitary distortion properties of the weak
$(p,q)$-quasiconformal mappings.
