In a reactor with feedback linearly proportional to the power level, the delayed neutrons permit the existence of unstable limit cycles. This means that, for linearly stable systems, the delayed neutrons can cause the system to become unstable for large enough disturbances. We demonstrate this analytically when the frequency of the limit cycle is near to the linear critical frequency. General criteria, based on the feedback transfer function, are given for the necessary existence of periodic solutions. Techniques for determining the stability of these periodic solutions are then shown. Examples are given for several reactor models.