  Let G be one of the Ricci-flat holonomy groups SU(n), Sp(n), Spin(7) or G_2,
and M a compact manifold of dimension 2n, 4n, 8 or 7, respectively. We prove
that the natural map from the moduli space of torsion-free G-structures on M to
the moduli space of Ricci-flat metrics is open, and that the image is a smooth
manifold. For the exceptional cases G = Spin(7) and G_2 we extend the result to
asymptotically cylindrical manifolds.
