Subpicosecond photoexcitation of CdS/HgS/CdS quantum dot quantum well nanoparticles at wavelengths shorter than their interband absorption (390 nm) leads to a photobleach spectrum at longer wavelengths (440-740 nm). The photobleach spectrum changes and its maximum red-shifts with delay time. These results are explained by the rapid quenching of the initially formed laser-excited excitons by two types of energy accepters (traps); one is proposed to be due to CdS molecules at the CdS/HgS interface, and the other trap is that present in the CdS/HgS/CdS well. The results of the excitation at longer wavelengths as well as the formation and decay of the bleach spectrum at different wavelengths support this description.