The strategy investigated in this work, is to reduce the computational requirements of the TSH method by relying on a multiple time step (MTS) algorithm. MTS techniques have first been introduced by Tuckerman et al. in the context of classical MD. The MTS scheme relies on a decomposition of the atomic or nuclear forces into different components with different characteristic time scales. This decomposition enables to calculate the slow components of the forces less frequently than the fast one, while maintaining a fully timereversible symplectic propagation. If the computational cost of the slow components is significant, large computational speed-ups can thus be obtained. This article is organized as follows. After introducing an MTS algorithm for TSH simulations in section II B, the new method is applied to the photorelaxation of protonated formaldimine (section III). The MTS-TSH algorithm is compared to standard TSH simulations both in terms of accuracy and computational cost. Finally, some concluding remarks and perspectives are given in section IV.