A new multi-code multicarrier code division multiple access (MC-MC-CDMA) system is proposed and analyzed in afrequency selective fading channel. By allowing each user to transmit an M-ary code sequence, the proposed MC-MC-CDMA system can support various data rates as required by next generation standards without increasing the interference which is common in general multicarrier CDMA systems. The bit error rate of the system is analytically derived in frequency selective fading, with Gaussian noise and multiple access interference. The results show that the proposed MC-MC-CDMA system clearly outperforms both single-code multicarrier CDMA (MC-CDMA) and single-carrier multi-code CDMA in a fixed bandwidth allocation.This indicates that MC-MC-CDMA can be considered for next generation cellular systems.