The presented work explores the evolution towards energy equipartition in models of star clusters with different initial degrees of velocity anisotropy. Our analysis has revealed several novel dynamical aspects, such as the rate of evolution towards energy equipartition depends on the initial degree of radial velocity anisotropy, and differs for the radial and the tangential components of the velocity dispersion. We have also found that the outermost regions of the initially isotropic system evolve towards a state of ‘inverted’ energy equipartition, which means that high-mass stars have a larger velocity dispersion than low-mass stars. This is due to the dependence of the tangential velocity dispersion on the stellar mass; the radial velocity dispersion shows no anomaly. Finally, we focused on the effects of different strengths of the Galactic tidal field and the role of primordial binaries. Our results shed further light on the link between the clusters’ internal kinematics, their formation and evolutionary history, and also add new fundamental elements to the theoretical framework needed to interpret the observational studies of stellar kinematics in globular clusters.