In this paper, we outline the extension of the MOESP family of subspace model identification schemes to the Hammerstein-type of nonlinear system. Two types of identification problem are considered. The first type assumes the (polynomial) structure of the static nonlinearity to be given and the task is to identify both the linear system dynamics and the unknown proportional constants in the parametrization of the static nonlinearity. The second type addresses the identification of both the linear dynamic part and the static nonlinearity, where only limited a priori information regarding the structure of the nonlinearity is available. The improved robustness properties of the algorithms developed for this second type of Hammerstein identification problem over existing correlation-based schemes is illustrated by a numerical example.