A binary asynchronous direct sequence spread spectrum multiple access system through Nakagami's m‐distributed channel is considered for non‐diversity receptions. Effects of fading and multiple access interferences on the average error probability are investigated. Approximation method to the average error probability is evaluated in two steps based on the moments of multiple access interferences and Nakagami distributions. Gauss quadrature rule is applied to evaluate the conditional probability conditioned on a fixed m‐distributed fading amplitude of the desired signal. Average error probability is then evaluated by the trapezoidal integration which integrates the conditional probability and the m‐distributed probability density function of the desired signal. This method provides a good approximation to the average error probability when the number of simultaneous users is large. Numerical results for the pseudorandom codes of code length 31 and Gold codes of code length 31 and 127 are presented.