The domains of stability predicted by Lyapunov's direct method and a modified semigroup method were compared with a direct numerical solution of a space-time nonlinear reactor system. The example employed the xenon-induced flux oscillation problem. It was found that the Lyapunov method and modified semigroup method were very conservative when compared with the numerical solution approach. No domain of stability was found with Lyapunov's method, while the semigroup approach showed a domain of stability nine orders of magnitude more conservative than that predicted by the numerical solution. / M.S.