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This paper presents an algorithm called Chains for separating temporal patterns of events that are mixed together. The algorithm is motivated by the task the auditory system faces when it attempts to analyse an acoustic mixture to determine the sources that contribute to it, and in particular, sources that emit regular sequences. The task is complicated by the fact that a mixture can be interpreted in several ways. For example, a complex pattern may issue from a complex source; or, alternatively, it may arise from the interaction of many simple sources. The idea pursued here is that the brain attempts to account for an incoming sequence in terms of short, fragmentary sequences, called chains. Chains are built as the input arrives and, once built, are used to predict inputs. A group of chains can coalesce to form an organisation, in which the member chains alternately generate predictions. A chain fails upon making an incorrect prediction, and any organisation it belongs to collapses. Several incompatible organisations can exist in parallel. The Chains algorithm thus remains open to multiple interpretations of a sequence. Perceptual multistability, in which the perceptual experience of an ambiguous stimulus switches spontaneously from one interpretation to another, seems to require a similar flexibility of representation.