  We construct stable axially symmetric models of elliptical galaxies. The
particle density on phase space for these models depends monotonically on the
particle energy and on the third component of the angular momentum. They are
obtained as minimizers of suitably defined energy-Casimir functionals, and this
implies their nonlinear stability. 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.
