The space-independent dynamics of a reactor controlled by xenon poisoning is investigated. For reactor periods comparable to the delay in xenon production, the reactor is stable. For shorter periods, the reactor is unstable in the neighborhood of equilibrium unless the prompt xenon yield is a large fraction of the total xenon yield. The reactor power then goes into a stable oscillation. With increase in reactivity, the oscillations are of relaxation type, having the character of a sequence of widely separated power pulses controlled by xenon poisoning. The intensity of the power pulse generally becomes excessive when the reactivity approaches the total controlled by prompt xenon. Xenon burnup is of minor importance over the region controlled by the prompt xenon yield, although it leads to flux divergence at sufficiently short reactor periods. Analytical methods are developed for treating the dynamics of the system, and the prime importance of nonlinear effects is established. The need for data on the independent yield of both Xe135 and its 15 min isomer in fission of major reactor fuels is pointed out.