Unbalance in rotating machines causes malfunction of the system operation and it may leads to its failure. Therefore, the sources for imbalance should be investigated, identified, and measured to solve the mentioned challenges. Rotating unbalance appears when the geometric and the inertia axes of the rotor do not coincide, and as a result this causes self- excited vibrations. One of the methods to control and reduce the unbalances is utilizing automatic ball balancer (ABB). In previous studies, the stability and the dynamic behavior of ABB have been mostly investigated by using numerical methods, and the perturbation methods are applied only for stability analysis. Because of the advantages of the analytical methods in studying the dynamics of the systems, in the present study, for the first time the dynamic behavior as well as the stability of a rotor equipped with an ABB is analyzed by the multiple scales method. To this end, nonlinear equations of the systems are derived using the Lagrange’s equations and firstly, the multiple scales method is applied to investigate the stability of system and then the response of the system is achieved considering one and two terms of approximation. The results demonstrate that the stability analysis using the multiple scales method and the first method of Lyapanov lead to the same results. Moreover, the responses obtained by the multiple scales method and the mostly used numerical method, Rung-Kotta technique, are in a good agreement.