We prove that if an ALE Ricci-flat manifold $$(M,g)$$ is linearly stable and integrable, it is ($$L^2-$$)dynamically stable under Ricci flow, i.e. any Ricci flow starting ($$L^2\cap L^{\infty}-$$)close to g exists for all time and converges modulo diffeomorphism to an ALE Ricci-flat metric close to g. This is joint work with Alix Deruelle.