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This research deals with dynamics of a permanent magnet freely levitated above an excited high-T/sub c/ superconductor. Vertical restoring forces acting on the magnet were evaluated by analysis based on the critical state and flux flow models. The results show nonlinearity and frequency-dependence of the forces, which were observed in experiments. Vertical vibration properties of the system were also evaluated analytically by considering the above properties of the restoring forces. The results show good agreement with experimental ones, which include effect of the frequency-dependent stiffness on the resonant frequency, the primary resonance characteristics, stability of the steady-state motions and so on.