Abstract: We present some rigidity results for smooth actions of compact Lie groups on Poisson manifolds. In the case that the manifold is symplectic, we can prove rigidity using Moser's path method. For general Poisson manifolds, the path method works locally for tame Poisson structures but not in general. We can then use Nash-Moser to prove rigidity for Hamiltonian group actions of semisimple Lie groups of compact type. This talk is based on joint works with Nguyen Tien Zung and Philippe Monnier.