We study the flow response in large amplitude oscillatory shear of the molecular stress function (MSF) model that has recently been proposed by Wagner et al. [M.H. Wagner, P. Rubio, H. Bastian, The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release, J. Rheol. 45 (2001) 1387-1412]. The MSF model is derived from molecular theory and has only two parameters to describe the non-linear material response. The model predictions are analysed in both the frequency and time domain. It shows good agreement with experimental data for a linear high-density polyethylene melt. At low and medium strains, MSF model predictions are in excellent agreement with experimental data and predictions of a six-mode Giesekus model which has six parameters to describe the non-linear material response. At medium strains, the basic Doi-Edwards model, which has no non-linear parameters, already underpredicts the data. At high strains, the MSF model predictions agree slightly better with the experimental data than the Giesekus model. Surprisingly, however, it is the Doi-Edwards model that shows excellent agreement with experimental data at high strains. For the linear melt we consider, it outperforms the models that have non-linear parameters, both in the time and frequency domain. (c) 2005 Elsevier B.V. All rights reserved.