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SynopsisIn this paper, the predictions of the Pompom constitutive model in medium and large amplitude oscillatory shear (LAOS) are examined using Fourier transform rheology (FTR). FTR is commonly used in combination with small amplitude oscillatory shear to fit linear Maxwell parameters to dynamic moduli, and in this paper, this process is expanded to larger strain amplitudes and to further terms in the Fourier series. For both small and large amplitudes, these higher harmonics are dependent on the nonlinear Pompom parameters and the Pompom parameter space is explored to see how experimental oscillatory shear data can infer molecular detail. In the regime of small and medium strain amplitude, there exists an asymptotic solution to the Pompom equations which depends only on the ratio of the orientation and stretch relaxation times,