This article presents results of VLBI observations of regions of H2O maser activity in the Local Group galaxies M33 and IC10. Since all position measurements were made relative to extragalactic background sources, the proper motions of the two galaxi
es could be measured. For M33, this provides this galaxys three dimensional velocity, showing that this galaxy is moving with a velocity of 190 +/- 59 kms relative to the Milky Way. For IC10, we obtain a motion of 215 +/- 42 km/s 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.
