Four classical viscoelastic models are adopted to analyze the nonlinear free vibrations of moving belts. The models include Kelvin solid, Maxwell fluid, standard linear solid and Maxwell-Kelvin fluid. Two model-dependent parameters are given for each model. In terms of these parameters, general solutions of the free oscillation responses are given in closed forms for all these models. For the resulting amplitudes and frequencies, numerical simulations are performed to compare these viscoelastic models.