  We study the mean curvature flow of complete space-like submanifolds in
pseudo-Euclidean space with bounded Gauss image, as well as that of complete
submanifolds in Euclidean space with convex Gauss image. By using the
confinable property of the Gauss image under the mean curvature flow we prove
the long time existence results in both cases. We also study the asymptotic
behavior of these solutions when $t\to\infty$.
