We discuss which fraction of the matter flowing to the companion during a Roche lobe overflow phase can actually be accreted by the secondary star. Employing new evolutionary models for massive close binaries which include the effects of rotation for both components as well as angular momentum accretion and spin-orbit coupling, we propose a physical model to calculate the accretion efficiency in Case A and B systems. We provide examples showing that both cases, high and low accretion efficiency, do occur within these models, as it seems required by observed post-mass transfer systems. Furthermore, we discuss late evolutionary stages of such binaries, with emphasis on the formation of compact objects: what are their spin rates, which systems can produce black holes, which gamma-ray bursts?