Relay selection is a promising technique with which to achieve remarkable gains in multi-relay cooperative networks. Opportunistic relaying (OR) and selection cooperation (SC) are two major relay selection schemes for dual-hop decode-and-forward cooperative networks; they have been shown to be globally outage-optimal under an aggregate power constraint. However, due to channel fluctuations, the channel state information (CSI) used in the selection process may become outdated and differ from the CSI during the actual transmission of data. In this work, we study the effect of outdated CSI on OR and threshold-based SC (TSC) schemes under independent but not necessarily identically distributed Rayleigh fading channels. The source can possibly cooperate with the best relay for data transmission, with the destination performing maximal ratio combining of the signals from the source and the relay. In particular, we analyze the average symbol error probability (ASEP) of OR and TSC with outdated CSI by deriving approximate but tight closed-form expressions for the moment generating function of the end-to-end signal-to-noise ratio. We also investigate the asymptotic behavior of the ASEP. The results show that the diversity orders of OR and TSC reduce to one and two, respectively, due to the outdated CSI. However, TSC achieves full spatial diversity order when the relay-to-destination CSI is perfect. Finally, to verify the analytical results Monte Carlo simulations are performed, in which OR attains better ASEP than TSC in a perfect CSI scenario, while TSC is less susceptible to outdated CSI.