Abstract: The amplitude-frequency characteristics of nonlinear vibration of a serpentine belt drive system are investigated by means of both analytical and numerical methods. The vibration equation is established for a serpentine belt drive system which consists of a driving pulley, a driven pulley, a tensioner pulley and arm. The averaging method is extended to the multiple degree-of-freedom system, and the averaged equation is derived. For a specific example, the amplitude-frequency characteristics are obtained based on numerical integration of the vibration equation. It is found that the analytical results are in favorable agreement with the numerical solutions.