The bounded periodic behavior of the reactor power is studied for those instances when the equilibrium power is greater than the critical power level. Simple formulas are derived, for reactors with arbitrary linear feedback and no delayed neutrons, for the amplitude and frequency of the limit cycles. These quantities are shown to be related to the ratio of the equilibrium-to-critical power level and to the Laplace transform of the feedback kernel. Since the techniques used apply for arbitrary values of the fundamental component of the power oscillation, they are used to derive a describing function which is valid for large amplitude disturbances. Conditions for the existence of critical power levels and, hence, limit cycles are discussed. Formulae for investigating the stability of these limit cycles are also derived. Applications are made to the circulating fuel reactor and to the two-temperature reactor. It is also suggested that the results can be used in two practical situations: 1) When the oscillation amplitude is indistinguishable from the reactor noise, the power level can exceed critical; and 2) When the oscillation amplitude is large, the reactor can be used as a self-sustained pulse-modulated neutron source.