  We study the ellipticity and the ``Nekhoroshev stability'' (stability
properties for finite, but very long, time scales) of the Riemann ellipsoids.
We provide numerical evidence that the regions of ellipticity of the ellipsoids
of types II and III are larger than those found by Chandrasekhar in the 60's
and that all Riemann ellipsoids, except a finite number of codimension one
subfamilies, are Nekhoroshev--stable. We base our analysis on a Hamiltonian
formulation of the problem on a covering space, using recent results from
Hamiltonian perturbation theory.
