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When developing mathematical models, especially for control, the practical interest lies in relatively simple extensions of linear structures that offer improved modelling capabilities. In this paper a discrete-time input-output Hammerstein-bilinear structure is introduced and its properties are discussed in detail. It consists of a cascade connection of a static nonlinearity followed by a dynamic bilinear system. By combining advantages of constituent subsystems the Hammerstein-bilinear structure allows for both an input dependant dynamic behaviour (particular property of bilinear systems) and an increased flexibility of the steady-state characteristic (particular property of Hammerstein models) to be obtained simultaneously. Modelling capabilities of such structure are evaluated on an air-handling unit that is a part of an industrial heating, ventilation and air-conditioning system.