Event-based systems are developed and used to integrate components in loosely coupled systems. Research and product development have focused so far on efficiency issues but neglected methodological support to build such systems. In this article, the modular design and implementation of an event system is presented which supports scopes and event mappings, two new and powerful structuring methods that facilitate engineering and coordination of components in event-based systems. We give a formal specification of scopes and event mappings within a trace-based formalism adapted from temporal logic. This is complemented by a comprehensive introduction to the event-based style, its benefits and requirements.