Abstract: In this paper, the problem of the transverse nonlinearnonplanar oscillations of an axially moving viscoelastic belt with theintegral constitutive law are investigated in the case of 1:1 internalresonance. The governing equations of this problem are firstly derived withthe generalized Hamilton's principle to obtain the in-plane and out-of-planetransverse nonlinear oscillations of the axially moving viscoelastic beltneglecting the axially deformation. Perturbation analyses are carried out onthese partial differential governing equations with the multiscale methodand the Galerkin's approach to obtain four-dimensional averaged equationsand to analyze the stabilities of the solution in the dynamic system. Thesimulation results show the periodic motion, the quasi-periodic motion andthe chaotic motion in the transverse nonlinear nonplanar oscillations of theaxially moving viscoelastic belt.