An extensive series of calculations has been performed to study the approach to equilibrium of a neutron pulse in water and graphite. All calculations are based on multigroup diffusion theory with space dependence represented by the DB2 term. The time dependence of the neutron density, following a neutron burst at t = 0, is obtained by solving explicitly the time- and energy-dependent diffusion equation. The decay constants are thereafter computed and compared with the true eigenvalues of the scattering operator. Wherever possible, the theoretical calculations are compared with experiments.