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The authors propose an efficient moment generating function (MGF)-based method to evaluate the performance of generalized selection combining (GSC) over different fading channels. Employing a recently proposed method which is, however, only applicable to GSC diversity with independent and identically distributed branches, they derive a general MGF expression for the GSC output signal-to-noise ratio (SNR) for generalized fading channels, where the channel statistics in different diversity branches may be nonidentical or even distributed according to different distribution families. The resulting MGF expression is applicable to the analysis of the error probability, the outage probability, and the SNR statistics for GSC in a number of wireless communications scenarios with generalized fading. Numerical examples are presented to illustrate the application of the new analysis.