Recently, code division multiple access (CDMA) techniques have been utilised to achieve reliable multiuser communication in asynchronous shallow-water acoustic networks. Two different communication techniques, are considered. Both have their origins in spread spectrum principles and can offer significant benefits in such underwater environments, which are characterised by limited transmission bandwidth and are required to operate asynchronously with low signal-to-noise ratios. In direct-sequence (DS)-CDMA, spread data are transmitted at a single carrier frequency. In contrast, in multi-carrier (MC)-CDMA a set of carrier frequencies is employed to achieve frequency diversity. The proposed adaptive receiver architectures, based on the minimisation of the mean square error (MSE), integrate the functions of multi-access interference cancellation, equalisation and phase-carrier tracking. The performance of DS and MC-CDMA has been evaluated and compared under different simulation scenarios with respect to the multipath delay, Doppler broadening and number of users, indicating the effectiveness of each system in an underwater environment. Finally, analytical derivation of the BER performance of the MMSE multicarrier receiver in a Rayleigh-fading environment is presented.