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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 ([image omitted]) < vΣt is contained in the resolvent set of the operator, apart from some discrete eigenvalues. It is shown that a finite set of real time eigenvalues always exist. When the reflection coefficients at the two surfaces are equal, the decay constants decrease with increasing coefficients. The region Re ([image omitted]) > v Σt, 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.