In this paper, a two-relay full-duplex asynchronous cooperative network with the amplify-and-forward (AF) protocol is considered. We propose two distributed space-time coding schemes for the cases with and without cross-talks, respectively. In the first case, each relay can receive the signal sent by the other through the cross-talk link. We first study the feasibility of cross-talk cancellation in this network and show that the cross-talk interference cannot be removed well. For this reason, we design space-time codes by utilizing the cross-talk signals instead of removing them. In the other case, the self-coding is realized individually through the loop channel at each relay node and the signals from the two relay nodes form a space-time code. The achievable cooperative diversity of both cases is investigated and the conditions to achieve full cooperative diversity are presented. Simulation results verify the theoretical analysis.