  We show that as soon as a linear quantum field on a stationary spacetime
satisfies a certain type of hyperbolic equation, the (quasifree) ground- and
KMS-states with respect to the canonical time flow have the Reeh-Schlieder
property. We also obtain an analog of Borchers' timelike tube theorem. The
class of fields we consider contains the Dirac field, the Klein-Gordon field
and the Proca field.
