Is Wiener/Hammerstein system identification really nonlinear?

Currently, a number of methods exist for identifying nonlinear Wiener and Hammerstein systems. However, there is no attempt to address the fundamental questions of how nonlinear these identifications really are and why the existing methods work? In this paper, we try to answer the questions by investigating the objective function used to identify those systems. The results show that for both Hammerstein and Wiener identifications, the cost function is globally monotone has one and only one minimum.