Abstract: In this paper,the nonlinear dynamical characteristics for transverse vibrations of axially moving viscoelastic belt were investigated.The governing equations for the viscoelastic moving belt were derived in three-dimensional space.The method of multiple scales and the Galerkin's approach were applied directly to the partial differential governing equation of motion to obtain four-dimensional averaged equation.The results of numerical simulation demonstrate that there exist the periodic and chaotic motions of the axially moving viscoelastic belt.