An accurate approximation is obtained for the average probability of error In an asynchronous bleary direct-sequence spread- spectrum 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 KN, where K is the number of simultaneous transmitters and N is the number of chips per bit. For frequency-selective fading the computational effort grows linearly with the product KNsuKN. 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.