Nonstationary modes of direct and inverse passage through resonance of unbalanced rotor equipped with an imperfectly mounted autobalancing device (ABB) are investigated. Two mathematical models are considered. The first one is the passage of the critical region with constant angular acceleration, and the second one is the rotor motion under the influence of a constant external torque. The study of the first model revealed that the presence of ABB significant negatively influences on the process of direct passage through resonance, and the maximum amplitude of whirling in this case can exceed the maximum amplitude in the steady state case. At the same time, during inverse passage through resonance, the influence of ABB is positive, and the maximum amplitude of whirling is much less than in the case of the direct passage through resonance. The investigation of the influence of viscous damping in the ABB revealed that too small damping influences negatively on the transient process dynamics, delaying the time of the rotor resonant vibrations until the moment of their stop. The study of the processes of acceleration and rundown of the rotor according to the second model confirms the main conclusions obtained from the first model.