Modal characteristics of rotors are different from conventional modal characteristics of non-rotating structures. All dynamic characteristics of rotor systems are closely related to rotor rotation, and the modal parameters of rotor systems are also closely related to rotor rotation. Since the importance of the directivity of the modal parameters of rotor systems associated with rotor rotation has not been fully understood, the classical modal testing methods which apply to non-rotating structures have been applied to rotor systems to evaluate the modal characteristics of rotor systems. To identify the system parameters and to diagnosis the vibrations of rotating machinery it is important to clarify the modal characteristics associated with rotor rotation. Here the modal characteristics of asymmetrical rotor systems associated with rotor rotation are clarified. By using the complex modal displacement the forward and backward modes are properly identified. The mode shapes associated with forward and backward modes are discussed as the degree of asymmetry in the rotor varies. When curve veerings occur in the eigenvalue problem of an asymmetrical rotor system the abrupt but continuous changes of mode shapes are explained. The amplitude and whirl direction changes of forced responses at the given rotational speed to the changes of excitation direction for forward and backward modes are discussed.