We consider noncoherent multiuser detection techniques for a system employing nonlinear modulation of nonorthogonal signals. Our aim is to investigate near-optimum noncoherent multiuser-detection techniques that utilize the received signal structure while retaining reasonable complexity. Near-optimum approximations of the maximum-likelihood detector are investigated where the signal structure is reflected in the approximation techniques explored. Several implementations of noncoherent-soft interference cancellers are proposed and investigated, each of which exploits the signal structure in a specific way. We propose a class of detectors that employ selective filtering, a technique that exploits the a priori information that each user selects one of M signals for transmission. We show that selective filtering offers improved performance over the noncoherent counterparts of the existing near-optimum multiuser detectors. Both deterministic and blind adaptive implementations of selective filtering are considered. Numerical comparisons are provided to demonstrate the near-optimum performance of the proposed detectors.