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In this paper, we introduce a new differentiated successive-interference cancellation (DiffSIC) ordering technique for uplink multiple-user systems. Unlike classical successive-interference cancellation (SIC), DiffSIC is capable of differentiating users according to their priority or class of service by selecting a detection order that best fits the users' service profiles. In addition, DiffSIC is able to achieve the optimal SIC detection order that results in the best overall system performance. To develop DiffSIC, we introduce analytical methods toward finding instantaneous symbol error rates (SERs) for zero-forcing SIC (ZF-SIC) and minimum mean square error SIC (MMSE-SIC) detectors. Furthermore, we devise two procedures to reduce the computational complexity associated with the computation of SER and the enumeration of detection orders. We present a number of numerical results that clearly demonstrate the ability of DiffSIC to accomplish service differentiation and overall performance improvement in general.