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This paper generalises the theory of agent refinement from [1] to multi-agent systems in the presence of new coordination mechanisms extended with real time. The generalisation is such that refinement is compositional. This means that refinement at the individual level implies refinement at the multi-agent system level. Compositionality is an important property since it reduces heavily the verification process. Thus having a theory of refinement is a crucial step towards the verification of multi-agent systems' correctness.