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In most cooperative communications works, perfect synchronization among relay nodes is assumed in order to achieve cooperative diversity. However, this assumption is not realistic due to the distributed nature of each relay node. In this paper, we propose a new distributed space-time coded transmission (DSTCT) scheme for asynchronous cooperative communications under frequency-selective channels. First, a novel transmission protocol, in which each relay is labelled in delay-ascending order, is proposed. Second, the pairwise error probability and the design criterion of DSTCT are derived. Finally, based on the proposed transmission protocol and the design criterion, a new DSTCT scheme for asynchronous cooperative communications is proposed. Theoretical analysis and simulation results show that this scheme can achieve both full cooperative diversity and full multipath diversity.