This paper treats the dynamical evolution of a satellite orbiting a primary that is being despun by solar tidal friction. The results are then applied to Mercury and Venus. It is concluded that a wide variety of satellites would not have survived the solar tidal braking of these planets. Hence, the absence of satellites around Mercury and Venus is not a compelling reason for thinking that this has always been the situation. Satellites are lost by orbital decay and impact with the primary. It is likely that Mercury would retain a record of such an event on its surface.