An asymmetrical shaft supported by single-row deep groove ball bearings with clearance has nonlinear spring characteristics, rotating stiffness difference in shaft, and static stiffness difference in support at the shaft ends. When an asymmetrical rotor is supported horizontally, a harmonic excitation due to the unbalance and a double frequency excitation due to the coexistence of gravity and shaft asymmetry work simultaneously. As a result, this system becomes a nonlinear parametrically excited system with multiple periodic excitation forces. In this paper, nonlinear forced vibrations and parametrically excited vibrations are investigated theoretically and experimentally. Vibration characteristics of both isolated resonances and internal resonances are studied.