A new modal analysis method for general rotor systems with time-varying parameters is proposed. The essence of method is to introduce the modulated coordinates to derive the equivalent infinite order time-invariant matrix equation from the finite order time-varying matrix equation. Timevarying parameter equation is inevitable for general rotors, of which rotating and stationary parts both possess asymmetric properties. An extensive modal analysis method is rigorously developed for the infinite order time-invariant system and an approximate, yet effective modal analysis technique is introduced with the reduced order system, in order to derive four types of directional frequency response functions. It is shown theoretically that they can be effectively used for detection of the presence of system anisotropy and asymmetry. A numerical example with a simple rotor model and a flexible asymmetric rotor are also provided to demonstrate the theoretical findings and practicality of the proposed method.