Nonlinear response of linear and branched polymers has been investigated under medium strain amplitude oscillatory shear (strain amplitude range from 10% to 100%) with Fourier-transform theology. A power law relationship was found between the relative third intensity (I-3/I-1), which is an indicator of nonlinearity, and the strain amplitude at low and medium strain amplitudes. On a log-log plot, the intercept and slope Of I-3/I-1 Were investigated at different excitation frequencies and temperatures. Simulation results with three different constitutive equations [Giesekus, exponential Phan-Thien Tanner (E-PTT), pom-porn model] were also compared. Experimental results show that the intercept was affected by the excitation frequency and temperature, and the slope of I-3/I-1 for linear polymer remained constant regardless of molecular weight, molecular weight distribution, and excitation frequency in accordance with the predictions of the constitutive equations (Giesekus and E-PTT). It should be noted that the slope Of I-3/I-1 for branched polymer was lower than that of linear polymer, unlike the prediction of the pom-pom model. Among the molecular architecture and processing parameters (e.g., molecular weight, molecular weight distribution, frequency, and temperature), the slope of I-3/I-1, under medium amplitude oscillatory shear was found to depend only on the long chain branching, which means that it can be used as a measure of the degree of branching. The failure of the pom-pom model in predicting the nonlinear shear behavior was also pointed out. (c) 2007 The Society of Rheology.