Abstract
This article presents results of VLBI observations of regions of H2O maser activity in the Local Group galaxies M 33 and IC 10. Since all position measurements were made relative to extragalactic background sources, the proper motions of the two galaxies could be measured. For M 33, this provides this galaxy's three dimensional velocity, showing that this galaxy is moving with a velocity of 190 +/- 59 km s(-1) relative to the Milky Way. For IC 10, we obtain a motion of 215 +/- 42 km s(-1) relative to the Milky Way. These measurements promise a new handle on dynamical models for the Local Group and the mass and dark matter halo of Andromeda and the Milky Way.