  Analysis of the peculiar velocities of galaxies should take account of the
uncertainties in both redshifts and distances. We show how this can be done by
a numerical application of the action principle. The method is applied to an
improved catalog of the galaxies and tight systems of galaxies within
4$h_{75}^{-1}$ Mpc, supplemented with a coarser sample of the major
concentrations at 4$h_{75}^{-1}$ Mpc to 20$h_{75}^{-1}$ Mpc distance. Inclusion
of this outer zone improves the fit of the mass tracers in the inner zone to
their measured redshifts and distances, yielding best fits with reduced $\chi
^2$ in redshift and distance in the range 1.5 to 2. These solutions are based
on the assumption that the galaxies in and near the Local Group trace the mass,
and a powerful test would be provided by observations of proper motions of the
nearby galaxies. Predicted transverse galactocentric velocities of some of the
nearby galaxies are confined to rather narrow ranges of values, and are on the
order of 100 km~s$^{-1}$, large enough to be detected and tested by the
proposed SIM and GAIA satellite missions.
