This paper addresses the problem of joint detection for a spread-spectrum multiple-access system based on random permutations. The transmission channels are assumed to be frequency-selective and time-varying; moreover, these channels are unknown to the receiver. Consequently, the detection is achieved using an adaptive algorithm, whose objective consists of minimizing the minimum mean-square error. Alternatively, under the same hypotheses, an adaptive detector is also proposed for the DS-CDMA system, and compared with the previous detector. This comparison shows that, even if the detection is difficult in such a context for both detectors, the permutation-based method gives better performance.