Monodisperse linear and 3-arm star polyisoprene (PI) melts were investigated under dynamic oscillatory shear flow. Master curves of linear rheological properties, G'(omega) and G"(omega), obtained by small amplitude oscillatory shear (SAOS) testing and nonlinear rheological properties, Q(0) (omega), obtained by medium amplitude oscillatory shear (MAOS) testing, were created using the same shift factors by applying the time-temperature superposition (TTS) principle. Linear master curves of 3-arm star PIs were broader than those of linear PIs because of the contribution made by an additional relaxation mode due to arm retraction. This difference was clearer in nonlinear master curves. In nonlinear master curves (Q(0) (omega)), linear PIs showed only one peak corresponding to relaxation of the backbone chain, whereas two weak local peaks were observed for 3-arm star PIs. One peak at lower frequency reflected backbone relaxation and the other at higher frequency reflected branch relaxation. These findings confirm that Q(0) is a highly sensitive parameter for characterizing the effect of one branch by detecting backbone and branch relaxation modes. Based on the hierarchical relaxation concept of branched polymers, three characteristic relaxation times of 3-arm star PIs were determined from a nonlinear master curve: backbone relaxation time (tau(b)) from local maximum Q(0) at lower frequency, backbone Rouse time (tau(R,b)) from local minimum Q(0), and arm relaxation time (tau(a)) from local maximum Q(0) at higher frequency. Backbone relaxation times (tau(b)) from nonlinear master curves almost coincided with linear viscoelastic terminal relaxation times (tau(w)) from linear master curves within the limits imposed by experimental error. These relaxation times, especially tau(R,b),were used for molecular stress function (MSF) model predictions of 3-arm star PIs as a criterion parameter to determine the terminal relaxation mode of the backbone chain, and tau(R,b) was found to be a reasonable fitting parameter for the MSF model. Fitting results showed that the weak peak arising from the one branch could be quantified using the MSF model. However, both linear and 3-arm star PIs had the same beta value of 1, meaning a linear topology without a branch. It was concluded that the effect of only one branch could not be detected using beta values. Our results suggest the possibility of using the nonlinear parameter Q(0) for determining model parameters for constitutive model equations. (C) 2016 Elsevier Ltd. All rights reserved.