Magnetohydrodynamic (MHD) instabilities accompanied by magnetic islands in toroidal confinement devices are a major cause of energy confinement degradation and plasma disruptions. Since the amplitude of magnetic fluctuations increases as the mode rotation frequency decreases, clarification and control of rotational dynamics of MHD instabilities are of critical importance. Conventionally, these dynamics have been interpreted using torque balance models based on the competition between electromagnetic torques induced by external magnetic perturbations and driving torques in the plasma. However, recent experiments in JT-60U and LHD have revealed a characteristic evolution in which the rotation frequency of an MHD instability decelerates and subsequently accelerates. This behavior cannot be explained within the framework of a single torque balance model. The present work describes the features of this newly observed phenomenon.