  Quasifree states of a linear Klein-Gordon quantum field on globally
hyperbolic spacetime manifolds are considered. Using techniques from the theory
of pseudodifferential operators and wavefront sets on manifolds a criterion for
a state to be an Hadamard state is developed. It is shown that ground- and
KMS-states on certain static spacetimes and adiabatic vacuum states on
Robertson-Walker spaces are Hadamard states. Finally, the problem of
constructing Hadamard states on arbitrary curved spacetimes is solved in
principle.
