Let G be a non-compact real algebraic group and Γ < G a lattice. One purpose of this paper is to show that there is a smooth, volume preserving, mixing action of G or Γ on a compact manifold which admits a smooth deformation. In fact, we prove a stronger statement by exhibiting large finite dimensional spaces of deformations. We also describe some other, rather special, deformations when G = SO(1, n).