  We present new analytical distribution functions for anisotropic spherical
galaxies. They have the density profiles of the gamma-models, which allow a
wide range of central density slopes, and are widely used to fit elliptical
galaxies and the bulges of spiral galaxies. Most of our models belong to two
two-parameter families. One of these parameters is the slope gamma of the
central density cusp. The other allows a wide range of varying radial and
tangential anisotropies, at either small or large radii. We give analytical
formulas for their distribution functions, velocity dispersions, and the manner
in which energy and transverse velocity are distributed between orbits. We also
give some of their observable properties, including line-of-sight velocity
profiles which have been computed numerically. Our models can be used to
provide a useful tool for creating initial conditions for N-body and Monte
Carlo simulations.
