AbstractWe prove that if an ALE Ricci-flat manifold (M, g) is linearly stable and integrable, it is dynamically stable under Ricci flow, i.e. any Ricci flow starting close togexists for all time and converges modulo diffeomorphism to an ALE Ricci-flat metric close tog. By adapting Tian’s approach in the closed case, we show that integrability holds for ALE Calabi–Yau manifolds which implies that they are dynamically stable.