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In high-Tc superconducting magnetic levitation systems, a levitated body can keep stable levitation with no control. However, due to its low damping, the nonlinearity of the electromagnetic force can give rise to notable effects upon motion of the levitated body. Furthermore, the structure of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Thus, nonlinear characteristics can easily appear in elastic oscillation as follows. When the excitation frequency is the sum of natural frequencies of two modes, both of the two modes can resonate simultaneously. This phenomenon is called combination resonance. When the excitation frequency is a multiple of some mode's natural frequency, that mode can resonate. This phenomenon is called autoparametric resonance. These two resonances derive from the nonlinearity of the electromagnetic force. This research investigates how these two nonlinear resonances affect each other by using a beam that is levitated above superconducting bulks. From numerical and experimental results, it is figured out that, in fact, the above two nonlinear resonances cannot occur simultaneously and transition between them arises, under some conditions.