Methods for the analysis of neutron pulses slowing down in heavy media are presented. The Green’s function coupling method is reviewed and the application of a prompt-jump approximation to pulses slowing down in heavy media is discussed. In this paper, these methods are applied in particular to the analysis of the lead slowing down time spectrometer (LSDTS) and the application of this device to nondestructive fissile material assay (NDA). The effects of pulse width, spectrometer size, higher order spatial modes, and lead cross-section data on the calibration curve (t versus 1/√E, the dieaway curve N(t) versus t, and the time-dependent spectrum of the LSDTS are reported. For NDA, the assay of fresh light-water reactor (LWR), plutonium recycle, and fast reactor fuel pins, as well as spent LWR fuel pins, is studied. The effects of self shielding and pulse width on the discrimination capability of the LSDTS are assessed. Two energy ranges (27.6 to 43.6 eV and 10.3 to 16.3 eV) are proposed for the assay of mixed-oxide fuel where discrimination between 235U and 239Pu is required. An error analysis of NDA with lead spectrometers that includes the calibration surfaces which occur in the assay of mixed-oxide fuel pins is given.