A new approach for uncoupling the equations of motion typical for rotordynamical systems is presented. The method does not neglect the speed-dependent e!ects, such as gyroscopic e!ects, and can be particularly valuable in the controller design of actively controlled rotors. In the presence of hysteretic type of damping, the resulting uncoupled gyroscopic systems come with an equivalent viscous damping, equivalent in a sense of yielding the same natural frequency and decay rate. The approach is illustrated through three examples of technical interest: a Je!cott rotor with hysteretic damping, a Stodola}Green rotor, and a rotor of a small gas turbine. The generated results demonstrate that the developed approach is correct and straightforward.