In this paper, we present a cooperative system with amplify-and-forward (AF) multiple-full-duplex relays (FDRs) that receives and transmits signals simultaneously. In the first, we propose a new concept of delayed M-FDR relaying (M-D-FDR) scheme being able to achieve the full spatial diversity. At this time, we consider each delayed FDR receives a signal from source, adjacent relays and its delayed loop interference signal from its transmit antenna. In the second, we propose an efficient iterative successive interference cancellation (SIC) technique at destination that gradually cancels a delayed signal in order to fully obtain link diversity generated from M-D-FDR. Then, we investigate the various properties of the proposed M-D-FDR network by analyzing the pairwise-error-probability (PEP) analysis, especially in terms of signal-to-noise ratios (SNRs) between source to relays and source to destination links, respectively. Finally, we accomplish the performance evaluations to verify the analysis results and to compare with a non-delayed M-FDR (M-N-FDR) network.