Based on the stability and bifurcation theory of dynamical system, the lateral vibration differential equations of four-axis passenger coach, which have 17 degrees of freedom,were derived. The creep forces of wheel/rail in rolling contact were approximated by the linear creep theory of Kalker. The hunting stability and the bifurcation problems at superhigh speed of the passenger coach system were analyzed. The numerical results show that the method can obtain the critical speed of hunting instability, which gives the academic basis to bettering dynamic performance of lateral vibration and designing many parts of high-speed passenger coach.