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Hammerstein system identification is considered in presence of preload and dead zone nonlinearities. The discontinuous feature of these nonlinearities makes it difficult to get a single system parameterization involving linearly all unknown parameters (those of the linear subsystem and those of the nonlinearity). Therefore, system identification has generally been dealt with using multiple stage schemes including different parametrizations and several data acquisition experiences. However, the consistency issue has only been solved under restrictive assumptions regarding the identified system. In this paper, a new identification scheme is designed and shown to be consistent under mild assumptions.