  We explore an idea put forward many years ago by Zeldovich and Novikov
concerning the existence of compact objects endowed with arbitrarily small
mass. The energy-density of such objects, which we call ``Ghost stars'', is
negative in some regions of the fluid distribution, producing a vanishing total
mass. Thus, the interior is matched on the boundary surface to Minkowski
space-time. Some exact analytical solutions are exhibited and their properties
are analyzed. Observational data that could confirm or dismiss the existence of
this kind of stellar object is commented.
