Theory for diffeomorphisms of compact manifolds is an area of prime importance in dynamical systems. However, besides the results on circle diffeomorphisms, the rigidity in the other situation is far from well-known. In a joint work with L. Stolovitch (University Côte d’Azur), we show the local rigidity of the action by analytic isometries of compact real-analytic Riemannian manifolds under certain Diophantine condition. The proof is based on a Kolmogorov-Arnold-Moser scheme.