  We present the results of a study aimed at exploring the evolution towards
energy equipartition in star cluster models with different initial degrees of
anisotropy in the velocity distribution. Our study reveals a number of novel
aspects of the cluster dynamics and shows that the rate of evolution towards
energy equipartition (1) depends on the initial degree of radial velocity
anisotropy -- it is more rapid for more radially anisotropic systems; and (2)
differs for the radial and the tangential components of the velocity
dispersion. (3) The outermost regions of the initially isotropic system evolve
towards a state of `inverted' energy equipartition in which high-mass stars
have a larger velocity dispersion than low-mass stars -- this inversion
originates from the mass-dependence of the tangential velocity dispersion
whereas the radial velocity dispersion shows no anomaly. Our results add new
fundamental elements to the theoretical framework needed to interpret the
wealth of recent and upcoming observational studies of stellar kinematics in
globular clusters, and shed further light on the link between the clusters'
internal kinematics, their formation and evolutionary history.
