A method for the the derivation and truncation of correlation function
hierarchies for Markovian damped quantum-optical systems is presented
. The theory enables the inclusion of multiphoton scattering processes
which are ignored in conventional semiclassical theories. These produ
ce observable dynamical signatures which depend on characteristic scal
es of photon number. Applications of the theory to intracavity optical
parametric oscillation and second-harmonic generation are given.