  We study a new class of equilibrium two-parametric distribution functions of
spherical stellar systems with radially anisotropic velocity distribution of
stars. The models are less singular counterparts of the so called generalized
polytropes, widely used in works on equilibrium and stability of gravitating
systems in the past. The offered models, unlike the generalized polytropes,
have finite density and potential in the center. The absence of the singularity
is necessary for proper consideration of the radial orbit instability, which is
the most important instability in spherical stellar systems. Comparison of the
main observed parameters (potential, density, anisotropy) predicted by the
present models and other popular equilibrium models is provided.
