Our work deals with the analysis of the behavioural interoperability of systems in a designing context. Systems to be analysed are modelled as UML architectures in terms of assembly of components, the behaviour of which are defined by State Machines. We identify two interoperability levels: the absence of deadlock, and the fact that the required services and usage protocols are preserved. Our analysis consists in automatically transforming the behaviour of an architecture into a Labelled Transition System. The analysis of deadlock can be then performed through model checking tools. We identify relations enabling us to substitute components without analysing again the whole system, which leads us to define a notion of compatibility between components. This analysis technique checks if the interoperability of the new system is altered, preserved or improved: (i) the new system exhibits deadlocks: it is not interoperable any more (ii) it is deadlock free; (iii) it is deadlock free and moreover conforms to the previous one. Results are illustrated through a case study.