Abstract: To explore the lateral instability of the wheelset system, the gyroscopic effect and the influence of the primary suspension damping are considered, a dynamic model of the wheelset system with a nonlinear wheel-rail contact relationship is established, and the hunting stability, Hopf bifurcation characteristics, and migration transformation mechanism are investigated. The hunting instability critical speed of the wheelset system is obtained through the stability criterion. The central manifold theorem is used to reduce the dimensions of the wheelset system. Then the reduced wheelset system is simplified using the normal form method to obtain a one-dimensional complex variable equation with the same bifurcation characteristics as the wheelset system. The expression of the first Lyapunov coefficient of the wheelset system is derived theoretically, and the Hopf bifurcation type of the wheelset system can be judged according to its sign. The influence of different parameters on the Hopf bifurcation critical speed of the wheelset system is discussed, and the distribution law of supercritical and subcritical Hopf bifurcation regions of the wheelset system in two-dimensional parameter space is explored. Three typical Hopf bifurcation diagrams of the wheelset system are obtained by numerical simulation, which verifies the correctness of the distribution law of the supercritical and subcritical Hopf bifurcation regions of the wheelset system. The results reveal that the critical speed of the wheelset system decreases with the increase of the equivalent taper, increases with the increase of the longitudinal stiffness and longitudinal damping of the primary suspension, and first increases and then decreases with the increase of the longitudinal creep coefficient. The change of system parameters will change the type of Hopf bifurcation of the wheelset system, that is, the subcritical and supercritical Hopf bifurcations migrate and transform each other. The distribution law of the Hopf bifurcation domain of the wheelset system in two-dimensional parameter space has a certain guiding significance for wheelset parameter matching and optimization design.