We propose to integrate delay tracking into a successive interference cancellation (SIC) code division multiple access (CDMA) multiuser detector. Delay-robust SIC was initially proposed for CDMA multiuser detection when there exist time delay estimation errors. When the delay error is small, the true user signature vector can be approximately expanded around the estimated time delay as a linear combination of an estimated signature vector and an error vector. The amplitude of the error signal can be recursively estimated and cancelled in the multistage SIC iterations by using the tentative feedback decisions. Since the relative amplitude of the error signal provides information about the delay error, we propose the application of error signal feedback to improve the delay estimation. In a sliding window implementation, the delay-robust SIC is used to track multiple time varying user delays. For constant or slowly varying channels, a soft-decision function can be used to improve the delay-robust SIC. For fast fading channels, a linear decision function is used. Delay-tracking results for both rectangular chip pulses and band-limited chip pulses are shown.