  Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One
purpose of this paper is to show that there is an smooth, volume preserving,
mixing action of $G$ or $\G$ on a compact manifold which admits a smooth
deformation. We also describe some other, rather special, deformations when
$G=SO(1,n)$ and provide a simple proof that any action of a compact Lie group
is locally rigid.
