This paper investigates the dynamic behaviour of a rotordynamic system incorporating stiffness nonlinearity in the supporting bearings. The system model comprises a horizontal Jeffcott rotor mounted on symmetrically located ball bearings. The nonlinear radial stiffness of the bearing is estimated based on the Hertzian contact theory. The harmonic balance approximations and the time-marching method are applied to solve the governing equations and to determine the steady-state dynamic response. The results show that a small nonlinear bearing stiffness provides benefits for the suppression of response in the high frequency range. A large damping coefficient in the bearing can reduce the peak response amplitude. A combination of a small bearing stiffness and a large bearing damping can assist in effective vibration suppression from rotor in a broad excitation frequency range. These results lead to a better understanding of the effects of stiffness nonlineari-ty and damping property of the bearing on vibration behaviour and hence benefit enhanced de-signs with desirable dynamic characteristics.