Abstract. A local invariant is a set of states of a transition system with the property that every action possible from each of its states takes the system back into the local invariant, unless it is an ‘exit’ action, each of which is accessible from every state in the set via a sequence of non-‘exit’ actions. This idea supports a form of abstraction construction, abstracting away from behaviour internal to the local invariants themselves, that involving their non-‘exit’ actions. In this way, for example, it is possible to construct from a system one which exhibits precisely the externally visible behaviour. This abstraction is reminiscent of hiding in process algebra, and we compare the notion of abstraction with that of observational equivalence in process calculus.