In this study, the authors investigate the outage probability of underlay cognitive radio systems with relay selection. In particular, they consider a secondary multi-relay network operating in the amplify-and-forward (AF) mode and only the `best' relay is selected, which satisfies an index of merit. The proposed selection strategy takes into consideration the effect of primary user (PU) interference. That is, the authors assume that the secondary multi-relay network is exposed to unwanted interference from a neighboring PU network. They derive a closed-form outage probability expression and further present a thorough asymptotic diversity order analysis of the underlying scenario. A simulation study is presented to corroborate the analytical results and to have further insight into the performance of the proposed selection strategy.