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An accurate approximation is obtained for the average probability of error in an asynchronous binary direct-sequence spreadspectrum multiple-access communications system operating over nonselective and frequency-selective Rician fading channels. The approximation is based on the integration of the characteristic function of the multiple-access interference which now consists of specular and scatter components. For nonselective fading, the amount of computation required to evaluate this approximation grows linearly with the product , where is the number of simultaneous transmitters and is the number of chips per bit. For frequency-selective fading, the computational effort grows linearly with the product KN2. The resulting probability of error is also compared with an approximation based on the signal-to-noise ratio. Numerical results are presented for specific chip waveforms and signature sequences.