The reduction of vibrations in rotary systems is necessary condition for the development of constructions with high quality requirements. Among the devices that are able to reduce rotor’s vibrations are automatic balancers with balls, liquid, etc. Autoequalizers with torus-shaped body contain one ball-shaped adjustment mass that can freely roll both in the ring direction and in the cross section. This enables reducing to the minimum the force of resistance at the ball’s moving, but simultaneously decreases the chance of launching the autoequalizer in the autobalancing regime. Experimental researches of the autoequalizer have shown that along with the working state in which the ball stops relative to the rotating body from the opposite to the imbalance side, there is another state in which the ball continuously moves relative to the body of the autoequalizer. It has been stated that the ball in the working state is influenced by forces that are aimed at moving it in the body of the autoequalizer towards the side opposite to the imbalance. The design of an autoequalizer that ensures working state in which at rotation the ball stops relative to the autoequalizer’s body opposite to the imbalance has been experimentally worked out. The autoequalizer is made up of the mathematical model with two differential equations. In the result of the calculations it has been proved that the ball of an equalizer with the torus-shaped body has at least two movement conditions one of which is a working state, and another one is a spare state.