  It is our purpose to study complete space-like self-expanders in the
Minkovski space. By use of maximum principle of Omori-Yau type, we can obtain
the rigidity theorems on $n$-dimensional complete space-like self-expanders in
the Minkovski space $\mathbb R^{n+1}_{1}$. For complete space-like
self-expanders of dimension $2$, we give a classification of them under
assumption of constant squared norm of the second fundamental form.
