We have developed a multiple time scale (MTS) quantum wavepacket propagation algorithm for the electron-nuclear dynamics in which the electron and nuclear motions are followed simultaneously. The large mass disparity between the electron and the nuclear degrees of freedom poses a problem when one propagates the total wavefunction using a single time step. The standard split operator propagation method requires a small time step to be used for stable propagation of the fast electronic degrees of freedom, which leads to an unnecessarily large number of propagations for slow nuclear motions. A new factorization of the time evolution operator based on the decomposition of the total Hamiltonian into the nuclear part and the electronic Hamiltonian is proposed. The MTS factorization allows one to choose the spatial grid size and the time step appropriate for each subsystem separately. The MTS algorithm is applied to a charge-transfer model for the evaluation of optical spectra and thermal rate constants. It is shown that the multiple time scale propagation gives correct results with moderate computational time savings.