From a transactional point of view, composite systems are component based applications in which each component has its own transaction management logic.These systems are highly relevant in practice since they are likely to be the standard architecture for many future distributed applications.Unfortunately,there is no appropriate conceptual framework in which to reason about such systems.Following up on existing work that addressed special cases of composite systems, in this paper we tackle the problem of general composite systems, i.e., those with arbitrary configurations.We propose a correctness criterion, develop a new proof technique that allows us to address arbitrary configurations, and discuss several important issues related to concurrency control in distributed systems.