The mathematical model of a statically and dynamically unbalanced rigid rotor supported on linear viscous-elastic bearings and equipped with à single-plane ball self-balancing device is constructed. For the rotor spinning with a fixed angular velocity we have obtained the conditions of existence and stability of stationary balance motion. The non-stationary behavior of the rotor both the case of spinning with a fixed angular velocity and the passing through the critical speed with the constant angular acceleration are investigated numerically. It is shown, that under specified constructional conditions both the static and dynamic unbalances can be completely compensated using one single-plane ABB.