  It has been proposed recently to observe the change in cosmological redshift
of distant galaxies or quasars with the next generation of large telescope and
ultra-stable spectrographs (the so-called Sandage-Loeb test). Here we
investigate the possibility of observing the change in peculiar velocity in
nearby clusters and galaxies. This ``peculiar acceleration'' could help
reconstructing the gravitational potential without assuming virialization. We
show that the expected effect is of the same order of magnitude of the
cosmological velocity shift. Finally, we discuss how to convert the theoretical
predictions into quantities directly related to observations.
