Summary: This correspondence analyzes the high signal-to-noise ratio performance of optimum multiuser detectors for synchronous direct-sequence spread spectrum with random spreading in an additive white Gaussian noise channel. Under very general conditions on the received powers, we show that the optimum asymptotic efficiency of a \(K\)-user system with spreading gain \(N\) converges to 1 almost surely as \(K\to\infty\), and \(K/N\) is kept equal to an arbitrary nonzero constant. Therefore, the asymptotic behavior of the minimum bit error rate is equivalent to that of a single-user system.