Generalized digroups are considered a nontrivial extension of the concept of group, thus one might think that many definitions and results on group theory can be naturally extended to generalized digroups. In this paper, we prove that it is not always true, since we do not have a version of Lagrange’s theorem for generalized digroups. On the other side, we propose and study Sylow-type theorems for generalized digroups.