A quantum-classical approximation, capable of describing the evolution of open quantum systems well beyond the applicability limits of Redfield theory is suggested. The theory is based on the short lifetime of the quantum correlations between the quantum and the classical subsystem, caused by energy dispersion (per degree of freedom) of the canonical bath. The resulting quantum-classical approximation has the form of two auxiliary differential equations and fully accounts both for the arbitrary long memory of the heat reservoir and detailed balance. These equations allow direct solution in the time domain without constructing/diagonalizing Liouville space operators, and, in combination with molecular dynamics techniques to simulate bath dynamics, may be applied to quantum subsystems with a fairly large number of levels. A simple example of a two-level system, coupled to a single correlation time canonical bath, was considered to demonstrate different regimes of approaching the canonical equilibrium state. (C) 2003 American Institute of Physics.