  We provide an axiomatic framework for Quantum Field Theory at finite
temperature which implies the existence of general analyticity properties of
the $ n $-point functions; the latter parallel the properties derived from the
usual Wightman axioms in the vacuum representation of Quantum Field Theory.
Complete results are given for the propagators, including a generalization of
the K\"all\'en-Lehmann representation. Some known examples of
``hard-thermal-loop calculations'' and the representation of ``quasiparticles''
are discussed in this general framework.
