  In this paper we analyze the problem of uniqueness for spacelike
hypersurfaces with constant higher order mean curvature in generalized
Robertson-Walker spacetimes. We consider first the case of compact spacelike
hypersurfaces, completing some previous results given in [2]. We next extend
these results to the complete noncompact case. In that case, our approach is
based on the use of a generalized version of the Omori-Yau maximum principle
for trace type differential operators, recently given in [3].
