We have presented a new algorithm for non-adiabatic molecular dynamics simulations that is based on Tully's FS-TSH method combined with an MTS scheme for the integration of the nuclear classical equations of motion. The MTS scheme is an extension of the CPMD implementation introduced by Liberatore et al. in Ref. 21, in which the decomposition of the forces in terms of slow and fast components relies on the use of different electronic structure methods (e.g. different DFT functionals). In order to adapt the MTS scheme to the TSH method, it is important to enable electronic transitions in between outer steps. This is achieved by pre-evaluating the transition probabilities during inner steps with a low-level LZ criterion. If a transition is detected, a high level calculation is triggered, to confirm (or not) the electronic transition.