A method for real-time stability monitoring is developed for supervising the steady-state operation of a boiling water reactor core. The decay ratio of the reactor power fluctuation is determined by measuring only the output neutron noise. The concept of an inverse system is introduced to identify the dynamic characteristics of the reactor core. The adoption of an adaptive digital filter is useful in real-time identification. A feasibility test that used measured output noise as an indication of reactor power suggests that this method is useful in a real-time stability monitoring system. Using this method, the tedious and difficult work for modeling reactor core dynamics can be reduced. The method employs a simple algorithm that eliminates the need for stochastic computation, thus making the method suitable for real-time computation with a simple microprocessor. In addition, there is no need to disturb the reactor core during operation. Real-time stability monitoring using the proposed algorithm may allow operation under less stable margins.