A phase-space representation of Bloch-Redfield theory is used to describe the dynamical evolution of quantum dissipative systems. The resulting Liouville operator equations are capable of incorporating both the master equation in eigenstate space and the stochastic equation in classical phase space, and thus provide a useful framework for mixing classical, semiclassical, and quantum dynamics for simulating complicated dissipative systems. Ln addition, the proper limit of quantum dissipation, the approximate nature of the second-order cumulant truncation, the detailed balance of quantum correlation functions, and the reduction of dissipation by a transformation of the bath Hamiltonian are investigated within the framework of phase-space Bloch-Redfield theory. (C) 1997 American Institute of Physics.