  Up to now, most planet search projects have concentrated on F to K stars. In
order to considerably widen the view, we have stated a survey for planets of
old, nearby brown dwarfs and very low mass stars. Using UVES, we have observed
26 brown dwarfs and very low mass stars. These objects are quite inactive and
are thus highly suitable for such a project. Two objects were found to be
spectroscopic binaries. Another object shows significant radial velocity
variations. From our measurements, we conclude that this object either has a
planetary-mass companion, or the variations are caused by surface features.
Within the errors of the measurements, the remaining objects are constant in
radial velocity. While it is impossible to strictly exclude an orbiting planet
from sparsely sampled RV data, we conclude that it is unlikely that these
objects are orbited by massive planets with periods of 40 days or less.
