Abstract: Impacts between the flexible rotor and stator will excite the internal resonance of the forward and backward modes, resulting in asynchronous vibration, i.e, intermittent contact between the rotor and stator. To reveal the internal resonance mechanisms of the forward modes and backward modes, a mathematical model of the rotor system is established, Runge-Kutta numerical solution is used to solve the equation of motion, and the event detection function is used to detect the contact and non-contact motions. Through the coordinate system transformation, the Campbell diagrams of the rotor system under the stationary coordinate system and the rotating coordinate system are obtained, and the internal resonance speeds in the forward modes and backward modes are analyzed. Through the numerically calculated bifurcation diagram, the trajectory and frequency domain characteristics of the rotor when the asynchronous contact motion occurs are analyzed. The results show that the main resonance amplitude jumps at the critical speed, and there are two asynchronous contact response speed ranges. The rotor exhibits a closed continuous precession law in the stationary coordinate system and a periodic motion law in the rotating coordinate system, and there is a frequency doubling relationship in the rotation coordinate system, and the system has 2∶1 and 3∶1 internal resonance phenomena. The numerical simulation analysis verifies the correctness of the rotating speed predictions corresponding to the internal resonance, and the rotating speeds corresponding to the internal resonance can be predicted by this calculation method to avoid the internal resonance phenomenon caused by asynchronous contact.