[en] Recently, β-decay half-lives have been calculated microscopically for approx. 6000 nuclei between the line of β-stability and the neutron-drip line. These rates are systematically shorter for neutron-rich nuclei than those predicted previously by the gross theory of beta decay. The new rates call, therefore, for reinvestigations of dynamical r- and n-process models, which up to now have been treated with the gross theory or even simpler assumptions on the beta strength function. Here we discuss the r-process in the He-burning shells of supernova explosions of massive stars, which have suffered so far from the fact that the time-scales, over which a sufficient neutron flux could be obtained, were too short for a complete r-process. It is shown that with the new β-half-lives this difficulty is largely removed and that explosive He-burning indeed is a convincing alternative to the classical r-process scenario. In fact we find excellent agreement with the observed solar system r-process abundances if some enhancement of heavy elements due to s-processing during hydrostatic He-burning, which certainly does happen in those stars, is included. (orig.)