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The automatic tensioner is an important component of the engine front end accessory drive system (EFEADS). It maintains the tension of the belt steadily and reduces the slip of pulley, which is benefit for improving the life of V-ribbed belt. In this paper, an EFEADS model is established which is considering with the hysteretic behavior and the asymmetry of friction damping of a tensioner. A four-pulley EFEADS is taken as a study subject. The dynamic responses of system, such as the oscillation angle of each pulley, the slip factor of pulley, the oscillation of tensioner arm and the dynamic belt tension are analyzed with symmetric damping and asymmetric damping tensioner. Meanwhile, the influence of asymmetric damping factors of tensioner on the dynamic response of EFEADS is also investigated.