Quasielastic neutron scattering experiments have been performed on polyisobutylene, trans-1,4-polychloroprene, and polyethylene in the energy range from 0.01 to 10 meV at temperatures far above the glass transition temperature T-g and on cis-1,4-polybutadiene near T-g. Similar to the previously reported results on cis-1,4-polybutadiene far above T-g, we observe in these polymers a slow process on a time scale from several tens to several hundreds of picoseconds which we term the E-process (or elementary process) as well as a fast process with a time scale of about a picosecond. me consider the relaxation time map of polybutadiene near and above the glass transition temperature to illustrate that the fast process is common for most glass-forming materials and that the E-process may be assigned to an elementary process involving local chain conformational transitions. Finally, we analyze the E-process in terms of a previously introduced jump diffusion model with damped vibrations, which is consistent with recent results of molecular dynamics simulations for bulk amorphous polymers, and Re discuss the possible mechanism of the conformational transitions.