Summary: A nonlinear group-blind technique is developed for joint detection of some given users' data in a CDMA uplink environment with the presence of unknown interference. This method performs the so-called ``slowest-descent search'' over a likelihood function of the desired users, starting from the estimate closest to the unconstrained maximizer of the likelihood function, and along mutually orthogonal directions where this likelihood function drops the slowest. Simulation results show that this new nonlinear technique offers substantial performance improvement over the recently proposed linear group-blind multiuser detectors with little attendant increase in computational complexity. The problem of group-blind multiuser detection in the presence of both unknown interference and impulsive ambient noise is also treated under the framework of slowest-descent search, with the aid of a novel subspace-based robust interference cancellation scheme. It is seen that this robust group-blind method significantly outperforms the robust blind multiuser detection scheme proposed recently.