A general problem of time-dependent neutron transport in a spatially heterogeneous medium is analyzed by two perturbation methods that have previously been applied to specialized problems. These “buckling” and “asymptotic” methods are shown to be equivalent in the sense that the asymptotic method leads to a time-dependent diffusion equation with constant coefficients, whereas the buckling method leads to the corresponding dispersion law. Two applications, the calculation of keff, and the derivation of a point reactor model are given. Also, the general results obtained here are shown, in several special cases, to reduce to the simpler results obtained previously.