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The system performance of the opportunistic relaying technique in amplify-and-forward cooperative systems with adaptive transmission over Rayleigh fading channels is analysed. Two rate-adaptive modulation techniques, continuous-rate and discrete-rate adaptive techniques, are considered. Closed-form expressions are derived for the average spectral efficiency, outage probability and the average bit error rate for two cases: independent and identically distributed (i.i.d.) fading links and independent and non-identically distributed (i.ni.d.) links. Using numerical evaluations, the performances of different cases are compared showing the advantages of each adaptive modulation technique in conjunction with the opportunistic relaying in a cooperative communication over both i.i.d. and i.ni.d. fading links.