Measuring the proper motions and geometric distances of galaxies within the Local Group is very important for our understanding of the history, present state and future of the Local Group. Currently, proper motion measurements using optical methods are limited only to the closest companions of the Milky Way. However, Very Long Baseline Interferometry (VLBI) provides the best angular resolution in astronomy and phase-referencing techniques yield astrometric accuracies of ~ 10 micro-arcseconds. This makes a measurement of proper motions and angular rotation rates of galaxies out to a distance of ~ 1 Mpc feasible. This article presents results of VLBI observations of regions of H2O maser activity in the Local Group galaxies M33 and IC10. 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. (Abridged)
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