  We study in detail the modes of a classical scalar field on a
Kerr-Newman-anti-de Sitter (KN-AdS) black hole. We construct sets of basis
modes appropriate to the two possible boundary conditions (``reflective'' and
``transparent'') at time-like infinity, and consider whether super-radiance is
possible. If we employ ``reflective'' boundary conditions, all modes are
non-super-radiant. On the other hand, for ``transparent'' boundary conditions,
the presence of super-radiance depends on our definition of positive frequency.
For those KN-AdS black holes having a globally time-like Killing vector, the
natural choice of positive frequency leads to no super-radiance. For other
KN-AdS black holes, there is a choice of positive frequency which gives no
super-radiance, but for other choices there will, in general, be
super-radiance.
