In　this　paper,　the　problem　of　the　transverse　nonlinear　nonplanar　oscillations　of　an　axially　moving　viscoelastic　belt　with　the　integral　constitutive　law　are　investigated　in　the　case　of　1:1　internal　resonance.　The　governing　equations　of　this　problem　are　firstly　derived　with　the　generalized　Hamilton＇s　principle　to　obtain　the　in-plane　and　out-of-plane　transverse　nonlinear　oscillations　of　the　axially　moving　viscoelastic　belt　neglecting　the　axially　deformation.　Perturbation　analyses　are　carried　out　on　these　partial　differential　governing　equations　with　the　multiscale　method　and　the　Galerkin＇s　approach　to　obtain　four-dimensional　averaged　equations　and　to　analyze　the　stabilities　of　the　solution　in　the　dynamic　system.　The　simulation　results　show　the　periodic　motion,　the　quasi-periodic　motion　and　the　chaotic　motion　in　the　transverse　nonlinear　nonplanar　oscillations　of　the　axially　moving　viscoelastic　belt.