Abstract: This paper describes a formal framework for Object-Oriented (O-O) modelling of mechatronic systems, whose main contribution is, on the one hand, to unify the modelling approaches for dynamical systems and for industrial control software and, on the other hand, to provide a definition of inheritance, a cardinal concept in object-orientation, which emphasises the behavioural conformity of basic and derived classes of objects. The proposed framework exploits the coalgebraic description of software artefacts to provide a connection between the behavioural approach for modelling dynamical systems and the O-O approach for software modelling and design. In particular, our definition of inheritance aims to allow control engineers to apply the design by extension methodology, widely used in software engineering, to the development of mechatronic components for manufacturing systems.