  A relativistic version of the Kubo--Martin--Schwinger boundary condition is
presented which fixes the properties of thermal equilibrium states with respect
to arbitrary space--time translations. This novel condition is a natural
generalization of the relativistic spectrum condition in the vacuum theory and
has similar consequences. In combination with the condition of locality it
gives rise to a Kaellen--Lehmann type representation of thermal propagators
with specific regularity properties. Possible applications of the results and
some open problems are outlined.
