We consider the problem of detecting the entrance of a new-user in a direct-sequence code division multiple access (DS/CDMA) system operating over a fading dispersive channel. This problem has received considerable attention in the recent past in that it arises in a number of different contexts, such as decentralized user acquisition and data detection, handoff algorithms, soft handover procedures, and cell-search in wideband-CDMA systems. The detection algorithms that we propose in this paper are based on the application of the generalized-likelihood-ratio-test (GLRT) and can be implemented based on the knowledge of the spreading code of the user to be detected. In particular, the proposed procedures do not require any prior knowledge of either the propagation channel impulse response or the timing offset of the user to be detected. We consider both the cases of user detection in the reverse link of a cellular system, wherein it is assumed that the subspace spanned by the signals of the existing previous users is known to the receiver and that of user detection in the forward link, wherein the mobile receiver has no prior knowledge on the multiaccess interference. With regard to the latter situation, we develop a detection algorithm that ensures a constant false-alarm rate with respect to the second-order statistics of the overall disturbance. The performance of the proposed detection structures is finally assessed through closed-form formulas and through some sample plots, showing, for a given probability of false alarm, the probability that the new user is detected.