Abstract The time eigenvalue spectrum of the one-speed neutron transport equation has been investigated in the case of an infinite slab with reflective boundary conditions and isotropic scattering. The region Re ( ) v Σ t , too, is mainly contained in the resolvent set of the operator, the continuous spectrum consisting of only a set of discrete lines. Further it is shown that a finite number of real decay constants also exist in this region. We also give an upper limit for the magnitude of these eigenvalues. The analysis is supported by numerical calculations.