The purpose of the present work is to investigate numerically the energy-time characteristics of γ and neutron radiation emitted from strongly screened fissile substances irradiated by pulsed bremsstrahlung. It is shown that when fissile materials are screened by a metal with a small or medium atomic number (e.g., aluminum and iron) the prompt and delayed neutrons provide the greatest information for monitoring fissile substances. When fissile substances screened by hydrogen-containing materials are irradiated, γ rays delayed with respect to the probe radiation pulse are emitted and can be an indication of the presence of fissile substances. The time intervals for detecting prompt and delayed neutrons and delayed γ rays are evaluated.