Abstract-This paper proposes relay selection to increase the physical layer security in multiuser cooperative relay networks with multiple amplify-and-forward relays, in the presence of multiple eavesdroppers. To strengthen the network security against eavesdropping attack, we present three criteria to select the best relay and user pair. Specifically, criteria I and II study the received signal-to-noise ratio (SNR) at the receivers, and perform the selection by maximizing the SNR ratio of the user to the eavesdroppers. To this end, criterion I relies on both the main and eavesdropper links, while criterion II relies on the main links only. Criterion III is the standard max-min selection criterion, which maximizes the minimum of the dual-hop channel gains of main links. For the three selection criteria, we examine the system secrecy performance by deriving the analytical expressions for the secrecy outage probability. We also derive the asymptotic analysis for the secrecy outage probability with high main-to-eavesdropper ratio. From the asymptotic analysis, an interesting observation is reached: for each criterion, the system diversity order is equivalent to the number of relays regardless of the number of users and eavesdroppers.Index Terms-Multiuser communications, multi-relay cooperative networks, multiple eavesdroppers, physical layer security, secrecy outage probability.