Dynamic behavior with the hysteresis of the levitation force of a magnet-superconductor system is investigated with application of an alternating magnet field. The effect of a resonance swinging and break-off of the samples from the levitation level is found. Subharmonic resonance associated with the nonlinear of levitation dynamics is shown to the system. The critical amplitude vs. the field frequency to the superconductor is discussed. Levitation is stable most when the sample is exposed to a low-frequency field. In this case a large amplitude of the alternating field is needed to break-off of the sample.