The investigation considers the behaviour of rotor-dynamic systems subjected to non-symmetric clearance effects based on a Jeffcott rotor model. Only the undamped case is treated. Free nonlinear vibrations as well as resonant oscillations are analyzed using the method of multiple scales. Particular attention is paid to the “normal-loose” rubbing condition due to the bearing clearance effects and a discontinuous radial stiffness model is employed to analytically model this problem. General expressions for the amplitude and phase modulating functions characterizing the non-stationary oscillations of orthogonal components of the displacement vector are obtained. Further, an associated stability analysis is performed for the nonlinear steady state rotor motions by considering the singular points. A numerical study encompassing the different effects of the system parameters is also presented.