Quantum systems that can be usefully partitioned into a subsystem interacting with a bath will be considered. For such systems, a quantum-classical Liouville description of the dynamics is assumed, while retaining the full quantum equilibrium structure of the system. The equations of motion may be cast in the form of a non-Markovian equation for the diagonal elements of the subsystem density matrix. The memory kernel in this equation accounts for all coherences in the system. The conditions under which the memory kernel decays rapidly as a result of averages over quantum or classical bath equilibrium structure will discussed. When such decay is rapid, it will be shown how a lift back to the full phase space results in a Markovian master equation of motion. This equation leads to a surface-hopping trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results will be illustrated by simulations of nonadiabatic chemical dynamics. R. Grunwald and R. Kapral, J. Chem. Phys., 126, 114109 (2007). R. Grunwald, H. Kim and R. Kapral, J. Chem. Phys., 128, 164110 (2008).