Periodic　and　chaotic　space　oscillations　of　an　axially　moving　viscoelastic　belt　with　one-to-one　internal　resonance　are　investigated　for　the　first　time.　The　Kelvin　viscoelastic　model　is　introduced　to　describe　the　viscoelastic　property　of　the　belt　material.　The　external　damping　and　internal　damping　of　the　material　for　the　axially　moving　viscoelastic　belt　are　considered　simultaneously.　The　nonlinear　governing　equations　of　motion　of　the　axially　moving　viscoelastic　belt　for　the　in-plane　and　out-of-plane　are　derived　by　the　extended　Hamilton＇s　principle.　The　method　of　multiple　scales　and　Galerkin＇s　approach　are　applied　directly　to　the　partial　differential　governing　equations　of　motion　to　obtain　four-dimensional　averaged　equation　under　the　case　of　1:1　internal　resonance　and　primary　parametric　resonance　of　the　first　order　modes　for　the　in-plane　and　out-of-plane　oscillations.　Numerical　method　is　used　to　investigate　periodic　and　chaotic　space　motions　of　the　axially　moving　viscoelastic　belt.　The　results　of　numerical　simulation　demonstrate　that　there　exist　periodic,　period-2,　period-3,　period-4,　period-6,　quasiperiodic　and　chaotic　motions　of　the　axially　moving　viscoelastic　belt　Copyright　©　2007　by　ASME.