Mon. Not. R. Astron. Soc. 000, 1-12 (2003) Printed 13 June 2003 (MN L A T E X style

We construct stable axially symmetric models of elliptical galaxies. For these models the particle density on phase space is a function of the particle energy and the third component of the angular momentum and is decreasing in the former. They are obtained as minimizers of suitably de ned energy-Casimir functionals, and this implies their nonlinear dynamical stability against axisymmetric perturbations. Since our analysis proceeds from a rigorous but purely mathematical point of view it should be interesting to determine if any of our models match observational data in astrophysics. The main purpose of these notes is to initiate some exchange of information between the astrophysics and the mathematics communities