Abstract: According to the invention, the object (34) is brought to a first inspection station (I to IV) in which the object is irradiated by thermal neutrons, the capture gamma radiation then liable to be emitted by the object and characterizing a chemical element of the substance to be detected is detected, if the intensity of said radiation exceeds a predetermined threshold, the object is brought to a second inspection station (V,VI), in which the object is irradiated by fast neutrons and the prompt gamma radiation then liable to be emitted by the object and characterizing the chemical element is detected, the energy of the fast neutrons being at least equal to that of prompt gamma radiation, in order to confirm or disprove the information obtained in the first station.