HD 36705 (AB Doradus) and HD 155555 (V824 Ara) are two nearby very active cool stars. Both have strong Li I (lambda)6708 resonance lines, implying high surface Li abundances, comparable to those of very young T Tauri stars. They also have late M-type visual companions which share their proper motion, as confirmed by new astrometric measurements presented in this paper. We have carried out intermediate resolution optical spectroscopic observations of the faint companions to HD 36705 and HD 155555. Our main result is that these M-type companions show large Li depletions, and we argue that the dramatic difference in Li abundance between the components of these visual binaries can be understood if they are in an evolutionary stage intermediate between T Tauri stars and Pleiades low mass stars.