The crucial strength of the component paradigm lies in the possibility to encapsulate behaviours. In this work, we focus on the observable behaviour of composite components which encapsulate the behaviour of (possibly large) assemblies of connected subcomponents. We first present our general component model which is equipped with a precise formal semantics allowing us to distinguish systematically different kinds of behaviours for ports, for components, and for component assemblies; technically we use UML2 notation for describing component structures and I/O-transition systems for behaviours. Then we investigate an efficient method for the computation of the observable behaviour of composite components which can circumvent the possibly infeasible intermediate computation of the usually complex behaviour of underlying assemblies if there are behaviourally neutral subcomponents. Finally, we utilise the fact that components are connected via ports such that checks for behavioural neutral...