The paper deals with the parameter identification of Hammerstein systems having discontinuous asymmetric nonlinearities (two-segment piecewise-linear with preload and dead zone). Application of a simple decomposition technique provides a special form of Hammerstein model with a minimum number of parameters. The identification is carried out with only one record of measured input/output data despite the dead zone. To demonstrate the feasibility of the identification method, some illustrative examples are included.