In this paper the normal-mode-expansion method is applied to the Boltzmann equation in plane geometry. The simple, isotropic, separable kernel is used. With such a kernel the energy-dependent thermalization theory is described in terms of singular integral equations in a way quite similar to that in the one-velocity approximation. In particular, the solutions of the Milne problem and of the two adjacent half-spaces problem allow the boundary conditions for the asymptotic neutron distribution to be determined.