In this paper we investigate the performance of a cooperative network in the presence of an eavesdropper (Eve). Alice and Bob communicate with the help of a relay, which can operate either in halfduplex (HD) or full-duplex (FD) mode. We account for the self interference at the relay when operating under FD mode. Our analysis focus in the case that the CSI of Eve is not available at Alice. Thus, we derive closed-form expressions for secrecy outage probability. Our results allow us to compare the performance of FD and HD cooperative scenarios under secrecy constraints and, despite the additional interference at the relay, show the advantages of FD relaying over HD. In addition, we also show that a cooperative network is more vulnerable if Eve is closer to Alice than to the relay.Index Terms-Physical layer security, full-duplex relaying, secrecy outage probability.