A method is presented for predicting the occurrence of a hysteresis phenomenon, which is observed in experimental results dealing with the instability of rotor-bearing systems. The method is based on the Hopf bifurcation theory. It is shown that the existence of a hysteresis phenomenon is dependent upon the system’s operating parameters. To this end, the effect of oil viscosity on the hysteresis phenomenon and its implications on the rotor-bearing instability are investigated. The results of a series of experiments illustrating the effectiveness of the prediction of the hysteresis phenomenon using the Hopf bifurcation theory are also presented.