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The exact symbol error rates (SERs) of several M-ary modulation schemes are obtained in a unified manner for mobile radio receivers employing dual-branch coherent equal-gain combining (EGC), where the received signals on each branch follow either similar or different fading distributions. Specifically, the cases considered are Nakagami-m, Rice, and Hoyt fading on both branches, but with not necessarily identical parameters, and mixed Nakagami-m/Rice and Nakagami-m/Hoyt fading; only the integer or half-integer values of the Nakagami-parameter are considered. While the previous exact expressions for the SERs of general M-ary modulations with L-branch EGC contained double integrals, the error probability expressions derived in this paper for the case of L=2 contain only a single integral. In addition, the derived probability distributions also allow the direct obtaining of other useful performance measures, such as the exact level crossing rates, average fade durations, and outage probabilities.