  We study the dynamical properties of spherical galaxies with surface
luminosity profile described by the R^{1/m}-law, in which a variable degree of
orbital anisotropy is allowed. The parameter m for the present models covers
the range [1,10]. For these models we study the self-consistently generated
phase-space distribution function (DF), and we derive - as a function of m -
the minimum value of the anisotropy radius for the model consistency (i.e., in
order to have a nowhere negative DF). Then we study the region in the parameter
space where the R^{1/m} models are likely to be stable against radial-orbit
instability, and we compare its size with that of the larger region
corresponding to the consistency requirement. For stable anisotropic models the
spatial and projected velocity dispersion profiles are obtained solving the
Jeans equation, and compared to those of the globally isotropic case, already
discussed in Paper I. The relevance of the results in connection with the
Fundamental Plane (FP) of elliptical galaxies is pointed out: the effect on the
projected velocity dispersion due to the maximum orbital anisotropy allowed by
the stability requirement is well within the FP thickness, and so no
fine-tuning for anisotropy is required. Finally, the Velocity Profiles are
constructed as function of the projected radius and for various degrees of
anisotropy, and their deviations from a gaussian discussed.
