Abstract: The stable range of the guideway natural vibrationfrequencies is studied by analyzing the Hopf bifurcation of thevehicle-coupled-guideway maglev system. The maglev system is controlled bythe cascade controller and the connection of the controller's parameters andthe frequencies is given. Based on the stable controller, the Hopfbifurcation point corresponding changeless system parameters and variableguideway natural frequencies is calculated by the numerical arithmetic. Thestable range of the guideway natural frequencies is obtained using bothnumerical arithmetic and simulation method. The qualitative restrictionbetween the system mass, controller frequencies, stiffness of the secondsubsystem and the guideway natural frequencies is explained.