Context : In nearby clusters early-type galaxies follow isotropic orbits . The orbits of late-type galaxies are instead characterized by slightly radial anisotropy . Little is known about the orbits of the different populations of cluster galaxies at redshift z > 0.3 . Aims : We investigate the redshift evolution of the orbits of cluster galaxies . Methods : We use two samples of galaxy clusters spanning similar ( evolutionary corrected ) mass ranges at different redshifts . The sample of low-redshift ( z \sim 0.0 - 0.1 ) clusters is extracted from the ESO Nearby Abell Cluster Survey ( ENACS ) catalog . The sample of high-redshift ( z \sim 0.4 - 0.8 ) clusters is mostly made of clusters from the ESO Distant Cluster Survey ( EDisCS ) . For each of these samples , we solve the Jeans equation for hydrostatic equilibrium separately for two cluster galaxy populations , characterized by the presence and , respectively , absence of emission-lines in their spectra ( ’ ELGs ’ and ’ nELGs ’ hereafter ) . Using two tracers of the gravitational potential allows to partially break the mass–anisotropy degeneracy which plagues these kinds of analyses . Results : We confirm earlier results for the nearby cluster sample . The mass profile is well fitted by a Navarro , Frenk & White ( NFW ) profile with concentration c = 4 . The mass profile of the distant cluster sample is also well fitted by a NFW profile , but with a slightly lower concentration , as predicted by cosmological simulations of cluster-sized halos . While the mass density profile becomes less concentrated with redshift , the number density profile of nELGs becomes more concentrated with redshift . In nearby clusters , the velocity anisotropy profile of nELGs is close to isotropic , while that of ELGs is increasingly radial with clustercentric radius . In distant clusters the projected phase-space distributions of both nELGs and ELGs are best-fitted by models with radial velocity anisotropy . Conclusions : No significant evolution is detected for the orbits of ELGs , while the orbits of nELGs evolve from radial to isotropic with time . We speculate that this evolution may be driven by the secular mass growth of galaxy clusters during their fast accretion phase . Cluster mass density profiles and their evolution with redshift are consistent with predictions for cluster-sized halos in \Lambda Cold Dark Matter cosmological simulations . The evolution of the nELG number density profile is opposite to that of the mass density profile , becoming less concentrated with time , probably a result of the transformation of ELGs into nELGs .