The contribution of this paper is threefold: first, it defines a framework for modelling component-based systems, as well as a formalization of integration rules to combine their behavior. This is based on finite state machines (FSM). Second, it studies compositional conformance testing i.e. checking whether an implementation made of conforming components combined with integration operators is conform to its specification. Third, it shows the correctness of the global system can be obtained by testing the components involved into it towards the projection of the global specification on the specifications of the components. This result is useful to build adequate test purposes for testing components taking into account the system where they are plugged in.