In　this　paper,　the　two-dimensional　nonlinear　dynamics　are　investigated　for　the　nonplanar　nonlinear　vibrations　of　an　axially　accelerating　moving　viscoelastic　beam　with　in-plane　and　out-of-plane　vibrations　by　the　harmonic　differential　quadrature　method　(HDQM).　The　coupled　nonlinear　partial　differential　equations　for　the　two-dimensional　nonplanar　nonlinear　vibrations　are　discretized　in　space　and　time　domains　using　HDQM　and　Runge-Kutta-Fehlberg　methods　respectively.　Based　on　the　numerical　solutions,　the　nonlinear　dynamical　behaviors　such　as　bifurcations　and　chaotic　motions　of　the　nonlinear　system　are　investigated　by　using　of　the　phase　portrait　and　the　bifurcation　diagrams.　The　bifurcation　diagrams　for　the　in-plane　and　out-of-plane　displacements　via　the　mean　axial　velocity　and　the　amplitude　of　velocity　fluctuation　are　respectively　presented　while　other　parameters　are　fixed.　Copyright　©　2014　by　ASME.