  We extend the earlier linear studies of cosmological peculiar velocities to
Friedmann universes with nonzero spatial curvature. In the process, we also
compare our results with those obtained in cosmologies with Euclidean spatial
sections. Employing relativistic cosmological perturbation theory, we first
provide the differential formulae governing the evolution of peculiar
velocities on all Friedmann backgrounds. The technical complexities of the
curved models, however, mean that analytic solutions are possible only in
special, though characteristic, moments in the lifetime of these universes.
Nevertheless, our solutions exhibit persistent patterns that make us confident
enough to generalise them. Thus, we confirm earlier claims that, compared to
the Newtonian studies, the relativistic analysis supports considerably stronger
linear growth-rates for peculiar-velocity perturbations. This result holds
irrespective of the background curvature. Moreover, for positive curvature, the
peculiar growth-rate is found to be faster than that obtained in a spatially
flat Friedman universe. In contrast, linear peculiar velocities appear to grow
at a slower pace when their Friedmann host is spatially open. Extrapolating
them to the present, our results seem to suggest faster bulk peculiar motions
in overdense, rather than in underdense, regions of the universe.
