The one-mode stochastic nuclear reactor model has been proposed by Bell to study fluctuations in neutron populations. The purpose of this model is to allow consistent space and energy corrections to point reactor stochastic results. The model has been extended to also cover fluctuations in captures and fissions. A time-dependent, Monte Carlo computer program has been developed to simulate these fluctuations for a one-velocity bare reactor system and to estimate parameters of the probability distributions. It has been shown that the one-mode model for neutron populations and captures gives excellent agreement with the Monte Carlo results. Both showed a correction of about 50% to the magnitude of the variance predicted by basic point reactor equations. The fission probabilities required a more careful examination, but the Monte Carlo results could be predicted by approximate solutions to the exact stochastic equations. The influence of spatial effects on the properties of persisting and nonpersisting chains in supercritical systems has also been examined. The one-mode model provides important corrections.