The time eigenvalue spectrum of the one-speed, isotropic scattering neutron transport equation has been studied for a homogeneous sphere with vacuum boundary conditions. There is a close relationship between the time eigenvalue problem and the criticality problem of the time independent equation for the same model. It is shown that this relation holds even when the time eigenvalues are complex. Using Carlvik's method to solve the criticality problem, it is shown that complex time eigenvalues do actually exist for this model problem. Thus the real eigenvalues found by van Norton(1)do not form the complete spectrum.