  We 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 to g exists for all time and converges modulo diffeomorphism to
an ALE Ricci-flat metric close to $g$. 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.
