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This paper investigates the capacity of generalized- K fading channels. This very general model describes accurately composite multipath/shadowing fading channels which are widely encountered in real-world environments. We derive closed-form expressions for three adaptive transmission techniques, namely, i) optimal rate adaptation with constant power, ii) optimal power and rate adaptation, and iii) channel inversion with fixed rate. The analytical expressions obtained match perfectly the results obtained by computer simulations. These expressions provide a good tool to assess the spectral efficiency of the aforementioned adaptive transmission techniques over composite channels.