Recently considerable efforts have been devoted to the implementation of these on-the-fly trajectory-based dynamics methods for the simulations of time-resolved spectroscopic signals of model and realistic systems by using the NRFs and DW formalisms, see the original papers and the reviews . For example, the ab initio TSH-DW methodology has been developed in Ref. However, it is well known that all mixed quantum-classical dynamics methods may suffer from a number of deficiencies and restrictions. For instance, the famous fewest-switches surfacehopping algorithm (FSSH) does not properly describe electronic decoherence . It is thus worthwhile to explore a possibility of using alternative quantum-classical methods for the onthe-fly evaluation of nonlinear spectroscopic responses, in the hope that these methods will better reproduce the effects related to electronic and vibrational coherences.