Invariant imbedding method is applied to compute the energy-dependent, time-dependent transmission and reflection of neutrons in slab geometry. A set of “characteristic functions” (which are a generalization of Chandrasekhar's X- and Y-functions) can be defined when the scattering kernel is degenerate. A computational scheme is outlined which makes use of these functions to obtain the time decay constant, the time-asymptotic leakage flux, and, for a steady-state case, the thermal utilization factor for a heterogeneous system.