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The impact of outdated channel state information (CSI) on the performance of variable-rate adaptive M-ary quadrature amplitude modulation in amplify-and-forward (AF) opportunistic relaying systems over time-variant Rayleigh fading channels is analysed. Two rate-adaptive modulation techniques are considered. In the first scheme, the relay and the transmission rate are selected according to the CSI at the receiver side. In the second scheme, whereas selection of the relay is based on the receiver's CSI, the transmission rate is selected based on the predicted CSI at the transmitter after the feedback delay. The impact of imperfect CSI prediction on the system performance is also evaluated. For each scheme, analytical expressions are derived for the average spectral efficiency, outage probability and the average bit-error rate under outdated CSI. Using numerical evaluations the performances of the considered rate-adaptive modulation schemes are analysed to illustrate the impact of outdated CSI on AF opportunistic relaying systems.