  Equilibrium states in galactic dynamics can be described as stationary
solutions of the Vlasov-Poisson system, which is the non-relativistic case, or
of the Vlasov-Einstein system, which is the relativistic case. To obtain
spherically symmetric stationary solutions the distribution function of the
particles (stars) on phase space is taken to be a function of the particle
energy and angular momentum. We give a new condition on this function which
guarantees that the resulting steady state has finite mass and compact support
both for the non-relativistic and the relativistic case. The condition is local
in the sense that only the asymptotic behaviour for energy values close to the
maximal energy value in the particle distribution needs to be prescribed.
