Chirp signals have been exploited extensively in radar and underwater acoustic (UW-A) communication systems for their robustness to multipath and superior correlation properties. We present a multiuser multicarrier chirp-division multiplexing (MU-MCDM) system which orthogonal chirp spread spectrum are utilized in frequency subcarriers for multiuser applications. Furthermore, orthogonal chirp transform (OCT) and discrete orthogonal chirp transform (DOCT) are developed for continuous and discrete implementations of MCDM systems. In addition, we design a maximum likelihood (ML) receiver capable of synchronization, channel estimation, and symbol detection. MU-MCDM systems consider factors, including preamble length, number of subcarriers, portion of pilots, guard period, and multiuser access scenarios to adapt time-variant UW-A channels. The bit-error-rate (BER) performance and adaptive transmission are evaluated in simulation studies. Therefore, we have demonstrated MCDM modulation systems in simulations that they improve performance of UW-A communications adaptively and support multiple users. Moreover, MCDM architectures can be applied in higher order modulations for providing higher transmission rates in UW-A channels.