Large amplitude oscillatory shear strain was applied to anionically synthesized linear polystyrene solutions in dioctylphthalate. The resulting torque was analyzed in Fourier space with respect to frequency, magnitude, and phase (Fourier-transform rheology). The concentration of the solutions was varied to achieve different degrees of entanglement. In addition, numerical simulations were performed using the Giesekus constitutive equation fitted on the basis of linear viscoelastic data. We found a good qualitative agreement between experiments and predictions; a quantitative agreement was reached for intermediate strain amplitudes. Some deviations were observed at very low strain amplitudes. We present a descriptive relation for the relative magnitude of the third harmonic as a function of strain amplitude using a modified damping function. From this relation we obtained a universal parameter that describes the scaling behavior law for the increasing non-linearity (e.g., measured by the relative intensity of the third harmonic with respect to the response at the excitation frequency) as a function of the strain amplitude. We found that the scaling exponent for the investigated linear polymer systems was independent of various factors. In addition, we analyzed the strain dependence of the relative phase of the higher harmonies. For vanishing strain amplitudes we define a property (Phi(3)(0) that should reflect the contribution of the different relaxation modes to the viscoelastic response, and thus, a potential correlation to polymer topology. (C) 2003 The Society of Rheology.