  Let \alpha_0 be an affine action of a discrete group \Gamma on a compact
homogeneous space X and \alpha_1 a smooth action of \Gamma on X which is
C^1-close to \alpha_0. We show that under some conditions, every topological
conjugacy between \alpha_0 and \alpha_1 is smooth. In particular, our results
apply to Zariski dense subgroups of SL_d(Z) acting on the torus T^d and Zariski
dense subgroups of a simple noncompact Lie group G acting on a compact
homogeneous space X of G with an invariant measure.
