The movement of the simplest model of a statically unbalanced rotor under the condition of the action of a constant external torque is considered, taking into account the forces of external and internal damping. Two modes of stationary motion of the rotor are investigated: synchronous whirling and asynchronous self-excited oscillations. Using the system of equations that describes the rotor dynamics in polar coordinates, conditions for the existence and stability of both types of stationary modes are obtained.