The propagation of quantum/classical molecular dynamics equations is investigated from two different points of view. One is to take into account the time-dependence of effective Hamiltonians of quantum and classical subsystems by the combination of Zhu and Zhao's time-independentlike split operator method [J. Chem. Phys. 105, 9536 (1996)] and a predictor-corrector technique. The other one is to introduce a time-independent quasi-Hamiltonian operator for the total system based on which new split-operator propagators are constructed. High-order quantum wave-packet propagators and the multiple time scale technique can be easily employed in our algorithms. Four new quantum/classical propagators are proposed and tested in a simple model system. It is found that combinations of our algorithms with high-order quantum propagators or the multiple time scale technique can give good results even with very large time steps. These new schemes will be particularly powerful in the case when the propagation of the classical subsystem is most time-consuming.