ABSTRACT. The local dilatation H_p at a boundary point of a quasiconformal mapping on a plane domain of arbitrary connectivity is defined and it is shown that there is always a substantial point p, such that H_p=H, where H is the boundary dilatation. Infinitesimal local boundary dilatation is also defined and it is shown that the sets of infinitesimally substantial and substantial boundary points coincide for all non-Strebel classes.