Up to now, most planet search projects have concentrated on G and 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. As it turned out these objects are very inactive and thus highly suitable for such a project. For 19 objects, we can exclude a planet with the mass of 3 M J , and a period of 100 days or less with a probability of more than 60%. For these objects, we can also exclude Pegasi-planets with a high probability. For another 4 objects, we can exclude at least a brown dwarf companion. One object is a double line spectroscopic binary, and one object shows significant radial-velocity variations that can not be caused by a normal stellar-spot. This object either has a planetary-mass companion, or the variations are caused by surface structures that are quite different from normal star-spots.