Stationary modes of motion of an unbalanced symmetric rotor equipped with the ball automatic balancing device are considered. For the rotor spinning with a fixed angular velocity we obtain the analytic conditions of existence of the balanced and nonbalanced stationary modes. The stability of the balanced mode is investigated by analysis of the variational equations of perturbed motion with respect to a rotating frame, the stability of the unbalanced ones — with respect to a polar frame. The twoparameter diagrams of stability of stationary modes are constructed by the Routh criterion.