Currently, BWR stability analysis is most often performed by application of system codes which provide the time evolution of the neutron flux or thermal power at a defined operational point (OP) after imposing a system parameter perturbation. However, in general, it is impossible to understand the real stability state of the BWR at a specific OP by application of system code analysis alone. Hence, we are searching for methods developed in the nonlinear dynamics field in order to reveal the nature of the BWR stability states when power oscillations are observed. A powerful method is bifurcation analysis. In this paper, we will demonstrate an example of a possible BWR instability phenomenon, which can be understood only in nonlinear terms.