The variational method is used to reduce the general time-dependent Boltzmann equation to a multigroup (with overlapping or nonoverlapping) form. The variation of the fundamental decay rate with material properties is then studied. The relation between energy and space transients in pulsed multiplying and pulsed moderating systems is investigated. To augment the theoretical treatment of the asymptotic decay in a pulsed multiplying system, the Nelkin buckling expansion solution for the Fourier transformed transport equation for 1/υ absorption is extended to include non-1/υ absorption and fission. The development of an improved calculational procedure (DP-L multigroup overlapping or nonoverlapping) for determining the space and time dependence of the neutron flux in pulsed multiplying systems is described. This method is then applied to the analysis of recent pulsed spectra measurements. The duration of the energy and spatial transients and the variation of the vector flux distribution from the center to the edge of an assembly are described quantitatively. It is demonstrated that spatial asymmetries in the flux could exist after the flux distribution appears asymptotic.