Abstract In this paper the Wiener–Hammerstein Benchmark is identified as a bilinear discrete system. The bilinear approximation relies on both facts that the Wiener–Hammerstein system can be described by a Volterra series which can be approximated by bilinear systems. The identification is performed with an iterative bilinear subspace identification algorithm previously proposed by the authors. In order to increase accuracy, polynomial static nonlinearities were added to the bilinear model input. These Hammerstein type bilinear models are then identified using the same iterative subspace identification algorithm.