In order to meet the requirements of a net centric warfare concept for the defence, the Swedish navy needs to develop new methods and systems for underwater communication. It is mandatory that important platforms like submarines, ships and unmanned or autonomous underwater vehicles (UUV), acquire links making them accessible nodes in the network as well as allowing them to co-operate. Several types of links can be exploited, e.g. electromagnetic, acoustic, and laser, among which the acoustic link could be regarded as the generally most usable one for underwater communications. We advocate that we need to explore systems for acoustic underwater communication that have the potential of transferring data at rates of the order kbits per second over distances of at least tenths of kilometers. To this end we develop signal processing algorithms designed for acoustic underwater communication using bandwidth efficient modulation schemes such as quadrature amplitude modulation having M symbols or signal waveforms, M-QAM. The channel severely distorts the signals due to multi-path propagation which results in intersymbol interference (ISI) affecting tens or sometimes hundreds of symbols. We describe the design of an adaptive decision-directed feedback equaliser (DFE) which can reduce the ISI and make the message decodable. We also treat the problems of symbol synchronisation and compensation for the Doppler effect. This work is in progress and more results will be presented in a forthcoming report. Here we give preliminary results from an analysis of experimental data. Using 4-QAM transmissions in the Baltic Sea east of Gotland we could decode symbols without errors at data rates up to 8000 bits · s-1 at ranges of 14 km. No channel coding was used which leaves a marginal for improvements.