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A nonlinear rotational motion model for n-pulley damped serpentine belt drive systems (SBDSs) was developed. The effects of the belt deflection along the contact arc of pulleys on the belt span tensions were considered. The methods for calculating the tensioner arm vibration and belt slipping on pulleys were introduced. The effects of belt damping on rotational vibration of tensioner arm and belt slipping on pulleys were studied. Numerical solutions for a 3-pulley SBDS indicate that the belt slipping at the steady states should be controlled to avoid belt slipping at transient states. The slip factors tend to decrease when the belt damping increases, and the possibility of the belt slipping can be controlled through adjusting the wrap angles of pulleys and the preload of the tensioner when the design parameters of SBDS remain constant.