The topic of this thesis is the use of multi-carrier modulation with code division multiple access (CDMA). The motivation of this work is to establish if the combination of multi-carrier modulation with CDMA has a performance advantage over a conventional direct sequence CDMA (DS-CDMA) communication system. In this thesis three types of multi-carrier CDMA are identified and the main work is concentrated on one particular combination, which is referred to as one chip per carrier multi-carrier CDMA system. This system itself, however can be split into different variations and an examination of two of these is made. The first of these one chip per carrier multi-carrier CDMA systems utilises the same number of carriers as the spreading sequence length. The carriers overlap and adjacent chips of the spreading sequence modulate adjacent carriers. There is no guard interval and therefore intercarrier interference occurs. If the receiver is synchronised and has a perfect estimate of the channel, it is shown that this multi-carrier CDMA system has comparable performance to a DS-CDMA system of the same bandwidth. It is further shown that it is simple to compute the minimum mean square error criteria as the equaliser consists of N one tap equalisers, where N is the number of carriers. The second system utilises many overlapping low data rate orthogonal carriers. The orthogonality of the carriers is maintained due to cyclically extended guard interval and the number of carriers is much higher than the spreading sequence length. After spreading, the data streams are interleaved onto the carriers to maximise diversity. A practical form of maximum likelihood detection for 64 users is described. It is shown from simulation results that when the system is used in conjunction with ½ rate (constraint length 7) coding and equal gain combining the system can support 64 users at 6 dB E₆/N₆ for a bit error rate of 2 x 10^-3. This compares with an equivalent DS-CDMA system which can only support 16 users for the same bit error rate and E₆/N_o. These results assume perfect channel knowledge and synchronisation. It is further shown that to provide high spectral efficiency in a coded system a high rate convolutional coding scheme is needed. A combined decoder/canceller is also presented. Finally, techniques to achieve synchronisation and channel estimation algorithms are presented. These algorithms are considered in conjunction with the second system. In the framework of synchronisation, methods are presented for frequency and timing synchronisation. For channel estimation, simulation results are presented for a simple channel estimator.