A set of state equations of the polarization index governing system with saturation nonlinearity is established for a hydroturbine in small perturbation. The dynamic behavior of the proportional-integral governor (controller) governing system with saturation is analyzed and the conditions for the existence of a Hopf bifurcation are obtained by using a simple nonlinear model. The stability condition, which must be satisfied in the governing system, is simulated and supported by numerical calculations. The analysis and simulation show that a supercritical Hopf bifurcation may exist in hydraulic turbine systems. The results of this paper can be considered as an explanation for the sustained oscillations recorded in hydroelectric power stations.