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This paper investigates subharmonic resonance, one of typical nonlinear phenomena, appearing in a high-Tc superconducting bearing system. In such low-damping systems having noncontact support by magnetic force, complex dynamical behaviors can be caused by nonlinearity of the magnetic force. In this study, the magnetic rotor, supported by a high-Tc superconducting bulk, is bound to a D.C. motor with a universal joint. According to the equation of motion, caused by the quadratic term of the levitation force, subharmonic resonance of the rotor can occur when the rotor rotates, not at its critical speed, but at twice its critical speed. This analytical prediction was confirmed by our numerical and experimental results. Additionally, our study also found occurrence of internal resonance induced by this subharmonic resonance. These findings beyond linear regimes can be important for the design of high-Tc superconducting levitation systems.