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.
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