We analyse the radial and tangential velocity fields in the Galaxy as seen from the Sun by using as a first approximation a simple axisymmetric model, which we then compare with the corresponding fields in a barred N-body model of the Milky Way. This provides a global description of these quantities missing in the literature, showing where they take large values susceptible to be used in future observations even for sources well beyond the Galactic center. Absolute largest proper motions occur at a distance slightly behind the Galactic Center, which are there 1.5 times larger than the highest local proper motions due to the Galactic differential rotation. Large proper motions well beyond the Galactic center are well within the current astrometric accuracy.