The rolling bearing has the advantages of low friction,withstanding large transient overloads and small volume,which makes it as a major bearing element for rotating machinery including aeroengines,gas turbines and rocket motors. The varying compliance (VC) vibration is an inevitable parametrical vibration due to timevarying stiffness from rolling element revolution. Hysteretic VC resonances resulting from the Hertzian contact supporting stiffness of bearings have been found in many related studies. The hysteretic jumping vibration not only affects the operational stability and safety of the rotor system,but also induces cracks and fatigue failures of the bearing and other components. In this paper,by analyzing the characteristics of dynamic timevarying stiffness of the ball bearing,a method for estimating the VC resonant intervals was proposed by employing the dynamic natural frequency of the system. Based on this method,the inherent associations between the dynamic stiffness and the bifurcation of complicated motions in primary resonances were revealed. It is found that the system may emerge strong internal resonance when the natural frequency values of different freedoms are close to the 1∶2,which induces period doubling response and even quasiperiodic and chaotic motions. This study may be beneficial to control the complicated resonant responses of ball bearings.