  We consider space-times which in addition to admitting an isolated horizon
also admit Killing horizons with or without an event horizon. We show that an
isolated horizon is a Killing horizon provided either (1) it admits a
stationary neighbourhood or (2) it admits a neighbourhood with two independent,
commuting Killing vectors. A Killing horizon is always an isolated horizon. For
the case when an event horizon is definable, all conceivable relative locations
of isolated horizon and event horizons are possible. Corresponding conditions
are given.
