In the medium amplitude oscillatory shear (MAOS) test, intrinsic nonlinearity Q(0)(omega) derived from Fourier-transform (FT)-rheology is an important material function for investigating the nonlinear responses of complex fluids. However, Q(0) consists of elastic and viscous components without phase information, such as complex modulus vertical bar G*vertical bar obtained from the small amplitude oscillatory shear (SAOS) test. In this study, we decomposed Q(0) into Q(0)' (x) and Q(0)'' (omega), as done for storage modulus G(0) and loss modulus G '' in the SAOS test. Furthermore, intrinsic-nonlinear tan delta(equivalent to tan delta(3,0)), which provides third-harmonic phase information, was calculated by dividing Q(0)'' by Q(0)'. First, we defined mathematically elastic nonlinearity Q(0)' and viscous nonlinearity Q(0)'', and then investigated the physical meanings of Q(0)' and Q(0)''. Second, we applied the intrinsic parameters Q(0)' and Q(0)'' to monodisperse polystyrene solutions. All intrinsic-nonlinear master curves of Q(0)'') and Q(0)'' (omega) for model solutions showed similar behavior in the terminal regime (at low frequencies). Unentangled polymer solutions had the same intrinsic-nonlinear master curves. However, although the intrinsic-nonlinear master curves of entangled polymer solutions superimposed well at low De (near the terminal regime), they deviated at high De due to different entanglement densities. Therefore, two characteristic times, MAOS relaxation time and inflection time (tau(N) and tau(inf)), were determined from intrinsic-nonlinear master curves by comparing with terminal relaxation time and Rouse time (tau(L) and tau(R)) obtained from linear master curves. The results showed that intrinsic nonlinearities from the MAOS test are sensitive to relaxation processes (terminal and Rouse) of polymer chains. Finally, master curves were compared with predictions by the molecular stress function (MSF) model and the Pom-Pom model. The single-mode predictions of these two models described behavior changes qualitatively. However, both failed to achieve quantitative predictions of Q(0)'') and Q(0)'' (omega). On the other hand, the multimode MSF model agreed well with experimental data from the terminal regime to the inflection time scale under the terminal relaxation mode assumption. (C) 2018 The Society of Rheology.