This paper describes the damping characteristics of rotor in two radial axis, which are passively stabilized by magnetic bearing. The equations of rotor dynamics are introduced considering the effect of anisotropic stiffness of bearing. From the solution of the equations obtained by applying the method of averaging, the damping characteristics variation of the angular velocity is related to the anisotropy of the stiffness. The limit speed at which the damping factor is equal to zero increases with the difference of bearing stiffness in two orthogonal axes in the plane perpendicular to the axis of the rotation. These relations are examined in an experiment on a one-axis-controlled magnetic bearing.