This paper investigates the dynamics of cooperative emissions in a cascade three-level system driven by an ultrashort laser pulse by solving numerically the full-wave Maxwell-Bloeh equations.The 4,4’-bis(dimethylamino) stilbene molecule is used as the model molecule because of its strong two-photon absorption property.The two-colour cooperative emissions are studied as functions of molecular number density and dephasing rate of the dipole coherence.The propagation effects on the evolution of the cooperative radiations are also taken into account.The cooperative radiations are enhanced for large number density of the molecule,while the fast dephasing of the dipole coherence reduces the intensity of the cooperative radiations and delays the emission times or even inhibits the formation of the emissions.The delay time of the radiation decreases with the increase of the molecular number density and the propagation distance.