Using a Rheometrics Fluids Spectrometer, the nonlinear viscoelastic behavior of aquaous poly(ethylene oxide)(PEO) solutions with large amplitude oscillatory shear deformation has been investigated by analyzing the strain amplitude dependence of the storage modulus and dynamic viscosity. In this paper, the strain limits of linear viscoelastic response were determined and the effect of angular frequency on these values was examined. The behavior of the storage modulus and dynamic viscosity with increasing strain amplitude waIn also compared in nonlinear viscoelastic region. Further, the nonlinear behavior was interpreted by introducing the nonlinear viscoelastic functions derived from the Fourier expansion of the stress wave. Finally, the nonlinear behavior indices were defined and the effect of angular frequency on these values was discussed. Main results obtained from this study can be summarized as follows : (1) The storage medulus has a much stronger dependence on the strain amplitude and begins to show a nonlinear behavior at a smaller strain amplitude range than does the dynamic viscosity. (2) The strain limits of linear response of the storage modulus and dynamic viscosity are ${gamma}$$_{EL}$ = 40~50% and ${gamma}$$_{VL}$ = 80~100%, respectively. These values increase with decreasing angular frequency at frequency range lower than the inverse of the characteristic time. (3) The nonlinear behavior takes place at strain amplitude range larger than the limits of linear response, where the higher harmonic terms of the nonlinear viscoelastic functions show an obvious effect. (4) The nonlinear behavior indices have the maximum values at a specific angular frequency, and the elastic behavior shows more remarkable dependence on the angular frequency than does the viscous behavior.