A numerical experiment of the transient neutron behavior following a source burst has been performed. The time-dependent Boltzmann equation (in the diffusion approximation without delayed neutrons) was propagated in time until asymptotic conditions were reached. The explicit time, space and energy solution was programed for the IBM-7094. Space-independent calculations of defined effective multiplication factors, neutron lifetimes and decay constants were performed for hydrogenous and graphite-moderated U235 or Pu239 systems. Seventy-three velocity groups were employed to detail spectral changes that occur in the approach to equilibrium. About 20 µsec and 150 µsec, respectively, were required for the energy modes to decay in the hydrogenous and graphite systems considered. The initial response of a cadmium detector is shown to be similar in multiplying and nonmultiplying assemblies and indicates the neutron slowing-down time to the cadmium resonance. No further structure in the cadmium-detector response due to the regenerative process was noted. The space-dependent properties of bare and reflected one-dimensional slabs were also briefly studied.