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Compositional multi-agent system design is a methodological perspective on multi-agent system design based on the software engineering principles process and knowledge abstraction, compositionality, reuse, specification and verification. This paper addresses these principles from a generic perspective in the context of the compositional development method DESIRE. An overview is given of reusable generic models (design patterns) for different types of agents, problem solving methods and tasks, and reasoning patterns. Examples of supporting tools are described.