In many realistic wireless channels the ambient noise is known through experimental measurements to be decidedly non-Gaussian, due largely to impulsive phenomenon. Frequently, code-division multiple-access (CDMA) transmissions are made over fading channels. This paper deals with the problem of multiuser detection in direct-sequence CDMA fading channels with impulsive noise. The robustification is based on the concept of M-estimators found in the robust statistics. A new M-estimator-based structure for noncoherent demodulation of differentially phase-shift keyed (DPSK) signals transmitted simultaneously via an asynchronous CDMA flat-fading channel and embedded in impulsive noise, is proposed and analyzed. The approach is corroborated with simulation results and the simulation results show that, in highly impulsive noise, the proposed detector with significant performance gain outperforms the linear decorrelating detector, the Huber, the Hampel and the alpha M-estimator based multiuser detectors with little attendant increase in computational complexity.