It should be noted that Miller, Stock and their coworkers used the mapping approach in combination with the DW methodology for the calculation of time-resolved spectra for several model systems described by linear-vibronic-coupling Hamiltonians 100,101,112 . As distinct from these works, we develop the on-the-fly DW-MM methodology: The SQC scheme employed in the present work transforms the mapping variables back to the occupation numbers, which allows us to obtain simple explicit expressions for the DW functions which are convenient for the on-the-fly simulations. This largely extends the applicability of the on-the-fly SQC/MM-DW methodology, which can be used for the description of photoinduced dynamics and spectroscopic responses in realistic molecular systems. In this work, we simulate TA PP spectra of two popular molecular systems 113 , azobenzene and cis-hepta-3,5,7-trieniminium cation (PSB4) .