Dynamic quenching of the intensity of dual-band fluorescence pulses is modelled using numerical solutions of the equations for the population matrix of a model molecule with five states. The state with the highest energy is assumed to be resonantly excited by light and two other excited states that are populated by subsequent relaxation processes are assumed to be the initial states for molecular transitions with emission of dual-band fluorescence photons. The model parameters for the molecule are chosen to match the typical parameters of molecules with intramolecular proton phototransfer. Quenching is treated as a consequence of nonradiative decay of the excited states of the fluorescing molecule owing to collisions with quenchant molecules. Examples of different dual-band fl uorescence quenching mechanisms for the model molecule are given, depending on the decay of particular excited states of the molecule involving nonradiative intramolecular transitions or transitions into states of the quenchant molecules. Keywords mathematical modelling fluorescence quenching dual-band fluorescence pulses intramolecular hydrogen bond proton phototransfer