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This study analyses the achievable cooperative diversity order of the distributed linear convolutional space-time coding (DLC-STC) scheme for time-frequency asynchronous cooperative networks. The authors first prove that perfect time or frequency synchronisation is impractical for cooperative networks with multiple relays serving multiple destinations even when the relays know all accurate time delays and frequency offsets. Then the DLC-STC scheme, in which the exact time synchronisation at the relay nodes is unnecessary, is introduced into this type of cooperative networks. This study proves that the achievable time-frequency asynchronous cooperative diversity order of the DLC-STC scheme with maximum-likelihood receivers is equal to the number of relays. Simulation results verify the analysis.