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Processes that occur in many biological systems are not synchronous, but are governed by asynchronous updating. Although some previous models of multi agent systems have incorporated asynchronous updating in an informal or implicit way, the importance of asynchronous behaviour has been largely overlooked. However, the update scheme chosen is very important in determining the overall system behaviour. We illustrate this point using several updating schemes in simple models. The implication is that care should be given to selecting an update scheme that is appropriate for the modelling application. We also observe that certain ordered asynchronous processes play a role in emergent modularity: an important process in the evolution of complexity in living systems.