  The increasing interest in nonequilibrium effects in condensed matter theory
motivates the adaption of diverse equilibrium techniques to Keldysh formalism.
For methods based on multi-particle Green or vertex functions this involves a
detailed knowledge of the real-time properties of those functions. In this
paper, we derive general properties of fermionic and bosonic multi-particle
Green and vertex functions for a stationary state described within Keldysh
formalism. Special emphasis is put on the analytic properties associated with
causality and on a detailed discussion of the Kubo-Martin-Schwinger conditions
which characterise thermal equilibrium. Finally we describe how diagrammatic
approximations and approximations within the functional renormalisation group
approach respect these properties.
