The question of nonlinear stability of stationary reactor systems is investigated by two methods. The first method is analytic and sets the theory of nonlinear stability on a firm mathematical basis. The second method makes use of an electrical analogy and is based on the stability criterion stated by Weinberg and Ergen for nonlinear mechanical systems. Both methods deal with reactor systems in which feedback may be nonlinear as well as linear. The effect of delayed neutrons is included in the treatment. The stability conditions previously derived by others are shown to be special cases of the criteria proposed in this paper.