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The author obtains closed-form expressions for the averages of the Gaussian Q-function and product of two Gaussian Q-functions over the generalised eta-mu and kappa-mu distributions. These results can be useful in many practical applications when evaluating error rate performances of communication systems operating in radio channels modelled by the eta-mu and kappa-mu distributions. The formulas are obtained in terms of Appell's (F1(middot) and Phi1(middot)) and Lauricella's (FD 3(middot) and Phi1 (3)(middot)) hypergeometric functions. As examples of application, the average symbol error rates of general order rectangular quadrature amplitude modulation (QAM) in middotmiddotmiddot and middotmiddotmiddot radio channels are evaluated.