Abstract: Nonlinear dynamical behaviors for transverse vibation of axially moving viscoelastic strings are investingated based on the Poincaré map and bifurcation diagram. The governing equation is derived for the viscoelastic string using the integral constitutive relation. The geometrical nonlinearity due to small but finite deformation is taken into account in the derivation. The Galerkin method is used to control the truncation error of the governing equation. Auxiliary variables are introduced to transform the truncated system into the form which is convenient to integrate numerically. The bifurcation diagrams of the Poincaré maps of the string center are calculated versus the amplitude of tension fluctuation, the axial traveling speed, the viscoelastic coefficient and exponent of the string material.