Abstract: Aiming at the problem of nonlinear dynamics in the wheelset system, this paper analyzes the Hopf bifurcation point of the system based on the Hopf bifurcation algebraic criterion of the wheel considering the gyroscopic action, that is, the expression of the linear critical speed of the serpentine instability of the wheelset system. Based on the bifurcation theory, the first and second Lyapunov coefficient expressions of the wheelset system are obtained. Combining with the shooting method, the bifurcation diagrams of the wheelset system with and without the gyroscopic action under different longitudinal stiffness are also obtained. Through comparison with the bifurcation diagrams of the wheelset system with and without gyroscopic action, it is found that under the same longitudinal stiffness, both the linear critical speed and the nonlinear critical speed of the wheelset system considering the gyroscopic action are greater than those of the wheelset system without considering the gyroscopic action, that is to say, the gyroscopic action can improve the motion stability of the wheelset system. Based on the Bautin bifurcation theory, this paper takes the longitudinal stiffness and longitudinal velocity as parameters. In this way, wheelset systems with and without gyroscopic action are obtained, as well as the topological diagrams of the migration mechanism from subcritical Hopf bifurcation to supercritical Hopf bifurcation, and then from supercritical Hopf bifurcation to subcritical Hopf bifurcation. By comparing the Bautin bifurcation topological diagrams of the wheelset system with and without gyroscopic action, it is found that the gyroscopic action will change the degenerate Hopf bifurcation of the wheelset system, which, however, has little action on the Bautin bifurcation topology of the wheelset system.