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Semi-blind channel estimation and equalisation algorithms for asynchronous multiple input multiple output (MIMO) systems are proposed. MIMO channels are estimated from the second-order statistics of the received signals subject to an ambiguity matrix and unknown time delays. Then some pilot symbols are used to resolve the ambiguity matrix and the time delays. Two methods are presented for equalisation: the direct method and the two-step method. The direct method equalises the symbols directly without explicitly estimating the channels, while the two-step method needs to estimate the channels before recovering the symbols. Only upper bounds for the channel orders and the time delays are needed for implementing the algorithms. Neither the knowledge of real channel orders nor precise synchronisation of different users is required, which makes the algorithm applicable to practical multiuser MIMO systems.