Work is aimed at the study of a rotor with a vertical axis and a fixed ball-type automatic balancer, whose body is placed concentrically in relation to the rotation axis. The rotor has disbalance that creates vibrations of the system. An automatic balancer with a torus-shaped body contains one ball-type corrective mass that freely rolls within the body of the automatic balancer both circle-wise and in cross-section. This reduces forces of resistance in the motion regime of a ball to the minimum, but simultaneously decreases the chance of putting the automatic balancer in motion. Experimental researches with the automatic balancer have proved that together with the working regime, when a ball stops in relation to the rotating body towards disbalance, there is a regime when a ball continuously moves in relation to the body of the balancer. A mathematical model containing four differential equations has been made for a rotor with an automatic balancer. The results of the calculations have shown that a ball of a balancer with a torus-shaped body has at least two motion regimes, one of which is a working regime, while another one is superfluous.