An eigenvalue-eigenfunction analysis of beryllium assemblies over a large buckling range has been performed in a discrete energy representation. Transverse harmonics and the treatment of the energy dependence of the transverse buckling are shown not to change the conclusions. The decay in small assemblies that do not have an asymptotic (discrete) eigenvalue is seen to be dominated by a highly excited region of the continuous eigenvalue spectrum. This is characterized as a pseudo-fundamental eigenvalue-eigenfunction and is seen to be responsible for the observation of experimental decay constants that are greater than the minimum interaction rate. The pseudo-fundamental eigenfunction is peaked at the Bragg energies and describes a trapping of neutrons at these energies for the intermediate times accessible to experiment. It is doubtful that the theoretical long-time buildup of near-zero-energy neutrons, seen as a peak at the lowest energy mesh point for the lowest “continuum” eigenfunction can be observed by experiment. Spatial effects are examined by comparing Marshak and zero-flux boundary-condition results. The Marshak boundary condition gives, for example, a 3% increase in the decay constant and a higher peak in the spectrum at the major Bragg energy for B2 = 0.0753 cm−2. A surface spectrum predicted by diffusion theory is seen to be in qualitative agreement with experiment. The P3 pseudofundamental eigenvalue is nearly identical to the diffusion theory result, lending support to the assumption that transport effects are not dominant for the times, energies, and assembly sizes considered here. Spectra at energies below the Bragg cutoff are very sensitive to the transport approximation used, but these energies are outside the experimental range and have a negligible effect on integral parameters, such as the decay constant. The major features of the theory are checked against experiment.