By a combined effort of neutron scattering and molecular dynamics simulation, we have recently shown the existence of a crossover from Gaussian to non-Gaussian character of the self-correlation function of hydrogen atoms in the α-relaxation regime of a glass forming polymer, polyisoprene (PI). Following these previous results, here we present new data displaying different features of the above mentioned crossover. In particular, neutron scattering and molecular dynamics simulations corresponding to another glass-forming polymer, poly(vinyl ethylene) (PVE), and simulation results about the effect of temperature and density on the crossover in PI. We found that PVE displays a similar behavior to PI, showing the generality of the crossover picture. Moreover, we have also found that for PI the main features of the crossover do not depend on temperature and density. These results can be rationalized in the framework of the anomalous jump diffusion model which was previously introduced by us for self atomic motions in the α-regime of glass-forming polymers. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]