Abstract: A differential equation is developed for expressing the motion of a rotor system with slow-varying mass, based on a theoretical study on the rub-impact dynamic characteristics of a rotor system with slow-varying mass in a centrifuge with large eccentricity under the action of linear collisional/frictional forces. The effects of changes in rotor speed and unbalance on the vibration of a rubbed/impacted rotor system are analyzed through numerical method. The periodical and quasi-periodical motions of rotor system with slow-varying mass are revealed and described at different aspects, and how their forms evolved and transformed are discussed. The results indicate that the rotor system with slow-varying mass is equivalent to a rotor system with time-dependent damping and stiffness, which has obvious quasi-periodical motion features in its rubbed/impacted process without a chaotic motion arising from the constant mass of rotor system.