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Due to the broadcast nature of wireless medium, wireless transmissions can be overheard by any undesired receivers with eavesdropping capability within source transmission range. A novel physical layer approach for secure wireless cooperative communications against eavesdropping is proposed in this paper. For an asynchronous cooperative communication network with a cluster of user nodes transmitting to a common destination, we propose an anti-eavesdropping space-time network coding (AE-STNC) scheme to prevent eavesdropping and overcome the problem of imperfect synchronization. In the proposed scheme, training symbols are first transmitted by the destination (D). Owing to channel reciprocity, each user node can obtain the channel state information (CSI) between itself and D, which is unavailable to the eavesdroppers. By exploiting such CSI, anti-eavesdropping encoding is designed for each user node to create high decoding error rate at the eavesdroppers and ensure successful decoding at D. Furthermore, the AE-STNC is designed to achieve full diversity at D. Power allocation subject to average power constraint is considered and the secure region against eavesdroppers is also investigated. Based on the proposed AE-STNC scheme, an anti-eavesdropping space-time-frequency coding (AE-STFNC) scheme is proposed for broadband asynchronous cooperative communications. Simulations are provided to verify the performance and security of the proposed transmission schemes.