In this paper, direct sequence spread spectrum multiple access (DS/SSMA) communication system employing serially concatenated trellis coded modulation (TCM) and continuous phase modulation (CPM) over flat Rayleigh fading channel are presented. The performance of this concatenated TCM/CPM DS/SSMA system is exploited by the theoretical analysis and numerical simulations. The results demonstrate that significant improvements in error probability of this DS/SSMA system over the system with single TCM or CPM of different modulation indices can be achieved under the same conditions.