The spectrum of time eigenvalues has been studied for one-speed neutrons in isotropically scattering spheres with a reflexion coefficientRin the interval −1 ≤R≤ 1. It is proved that a continuous spectrum exists in the Hilbert space. This continuum disappears if we suitably enlarge the function space. It is also proved that forR≤ 0 there are only discrete eigenvalues on the real axis. However, forR> 0 there is a continuum of eigenvalues beyond the Corngold limit. An expression is given for the lower boundary of the continuum, and it is supported through numerical calculations.