Existing multiuser code-division multiple-access (CDMA) detectors either have to rely on strict power control or near-perfect parameter estimation for reliable operation. A novel adaptive multiuser CDMA detector structure is introduced. Using either an extended Kalman filter (EKF) or a recursive least squares (RLS) formulation, adaptive algorithms which jointly estimate the transmitted bits of each user and individual amplitudes and time delays may be derived. The proposed detectors work in a tracking mode after initial delay acquisition is accomplished using other techniques not discussed here. Through computer simulations, we show that the algorithms perform better than a bank of single-user (SU) receivers in terms of near-far resistance. Practical issues such as the selection of adaptation parameters are also discussed.