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Opportunistic relay selection is considered as an efficient approach to implement cooperative communication in multi-relay cooperative networks owing to its low implementation complexity. However, due to channel fluctuations, the channel state information (CSI) employed in relay selection process may differ from the exact CSI in data forwarding, in other words, the CSI is outdated. Addressing this issue, this paper focuses on the design of relay selection strategies in decode-and-forward (DF) cooperative networks with outdated CSIs being available in relay judgement, as well as their performance analysis. We resort to two main cases, 1) only outdated CSIs are available in relay selection process; 2) both outdated CSIs and statistical channel information are available in selection procedure, and propose three different relay selection schemes. The expressions of outage probability are derived, and asymptotic analysis in high SNR region is also carried out. Simulation results are finally provided, which not only validate our theoretical analysis, but also shed light on the way of designing relay selection strategies in various scenarios.