Galaxies inhabiting a cluster environment experience significant evolution in their orbital motions throughout time; this is accompanied by changes in the anisotropy parameter, measuring the relative importance of radial and tangential motions for a given class of objects. Along with orbital changes, galaxies in clusters are well known to undergo severe alteration in their hot/cold gas content and star formation properties. Understanding the link between the changes in the internal properties of galaxies and their orbital motion is of crucial importance in the study of galaxy evolution, as it could unveil the primary mechanism responsible for its environmental dependence. Do the changes in the internal properties happen in parallel with those in the orbital motion? Or are the orbital features at the time of infall that determines the fate of the member galaxies? Alternatively: are the properties of galaxies at a given time related to the coeval orbital anisotropy or are they better related to the anisotropy at infall? In order to answer these questions, we studied the orbital evolution of different galaxy populations in the semi-analytic models of Guo et al. applied on to the Millennium Simulation. For each class of objects, characterized by different internal properties (such as age, star formation rate and colour), we studied the anisotropy profile at redshift zero and its evolution by tracing the progenitors back in time. We conclude that the orbital properties at infall strongly influence the subsequent evolution of the internal features of galaxies and that the overall anisotropy of the galaxy population tends to increase with time.