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Using OFDM and space-time coding to achieve asynchronous cooperative diversity has been proposed by Mei et. al. and Shin et al, where orthogonal space-time block codes, Alamouti code in particular, were used at relay nodes. This proposed space-time coding can not achieve the multipath diversity when the channels from nodes to nodes are frequency selective fading. In this paper, we also consider asynchronous cooperative communications where the channels are assumed to be frequency-selective fading. We design high rate distributed space-frequency codes to achieve both full asynchronous cooperative diversity and multipath diversities.