The thermalization of neutrons in a finite medium is investigated to give a foundation for reactor calculations. The theory has been made free from the assumption that the energy spectrum of the flux is uniform throughout the medium. The flux is composed of several components, each having a definite spectrum and an associated diffusion length which are to be determined as an eigenmode and a corresponding eigenvalue respectively. It is seen that the Hurwitz-Nelkin spectrum derived under the assumption of flux separability corresponds to the component having the largest diffusion length, which is reached asymptotically in the region far from the source or the boundary. In the case of a noncapturing medium the eigenvalue problem determining diffusion lengths has been solved rigorously, and for weak absorbers a perturbation method has been developed. It is pointed out that the spectrum in a reactor is constituted by superposing the Hurwitz-Nelkin spectrum upon the others having smaller diffusion lengths, the latter being the contribution from the source distributed continuously near the point considered.