  We study the motion of an $n$-dimensional closed spacelike hypersurface in a
Lorentzian manifold in the direction of its past directed normal vector, where
the speed equals a positive power $p$ of the mean curvature. We prove that for
any $p\in (0,1]$, the flow exists for all time when the Ricci tensor of the
ambient space is bounded from below on the set of timelike unit vectors.
Moreover, if we assume that all envolving hypersurfaces stay in a precompact
region, then the flow converges to a stationary maximum spacelike hypersurface.
