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This paper introduces a parallel/sucessive interference cancellation scheme for multi-carriers code-division multiple access (MC-CDMA) in the case of a downlink transmission, that reduces the degrading effect on the desired user of interference from the other users who share the same channel. The implementation complexity of the scheme is linear in the number of users and operates on the fact that parallel processing simultaneously removes from each user a part of the interference produced by the remaining users accessing the channel the amount being proportional to their reliability. The parallel processing can be done in multiple stages. The proposed scheme uses an hybrid interference cancellation combining the advantages of these two schemes: parallel interference cancellation (PIC) and successive interference cancellation (SIC). The hybrid scheme (S-PIC) is faster, reliable and it reduces the computational load. Simulation results are given for different scenarios.