This is the second of a series of papers on the numerical solution of Einstein's equations for the dynamical evolution of a collisionless gas of particles in general relativity. This paper deals mainly with applications to spherical star clusters. Previous studies were restricted to static equilibria and linear perturbations. We bring together the tools of numerical relativity and N-body particle simulation to follow the full nonlinear evolution of such dynamical systems. We investigate the stability of equilibrium configurations. We present strong numerical evidence that, as in the case of fluid stars, the binding energy maximum along an equilibrium sequence does in fact signal the onset of dynamical instability. We explore the fate of unstable clusters, including those that collapse to black holes. We find that even in the case of extremely centrally condensed configurations with extensive Newtonian halos, an appreciable fraction of the total cluster mass collapses to a central black hole in a few dynamical times. This occurs because of the "avalanche effect" predicted by Zel'dovich and Podurets. The result may be important for the origin of quasars and active galactic nuclei via the collapse of dense star clusters to supermassive black holes. We discuss the dynamical stability of Newtonian polytropic clusters and report numerical evidence confirming that all equilibrium polytropes (even those whose distribution function increases with energy) are stable. We explore violent relaxation in the relativistic domain. A collisionless configuration can either achieve virial equilibrium via this mechanism or else collapse to a black hole. The outcome of such processes in the early universe may be relevant to the missing mass and dark matter problems.