Monte Carlo simulations were used to show that even very small explosives (<100g) can be detected by monoenergetic neutron backscattering with resonance penetration (MNBRP) at a depth well beyond 30 cm when time slicing is used for background suppression. At the present state of technology no other nuclear method appears to have a comparable sensitivity or penetration capability. This method has been successfully tested experimentally at a depth of 16.5 cm. A substantial simplification of the detection procedure could be achieved either by taking advantage of the time shadow rather than the geometric shadow or by applying neutron threshold detectors. Using a threshold detector could simplify the application, too.