The paper deals with the research of an autoequalizer with a vertical axis, and its body is placed with a relatively eccentric rotation axis. Autoequalizers with a 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 the forces that are aimed at moving it in the body of the autoequalizer towards the side opposite to the imbalance. The closer the ball is to the optimal state, the less the volume of tangential force influencing the ball is. 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. A patent of the autoequalizer design has been obtained. 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 the 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.