Event-based systems are used in a wide variety of applications such as digital libraries, stock tickers, traffic control, or facility management. Composite events have been introduced to capture richer situations. Composite events in different systems seem to follow a common semantics. However, the evaluation semantics of the considered events may differ heavily according to the approach chosen. We propose a parameterized event algebra that describes the detailed semantics of composite events. We define the event operators that form composite events and we introduce parameters for event instance selection and event instance consumption. These parameters serve as a support for handling duplicates in both primitive and composite events. The event algebra provides a foundation for - a (meta) language for events - adapting to changing systems/settings - meta-system (similar meta-search) Our approach flexibly supports the integration of event-based applications and changing event sources without the need to redefine user profiles.