The thesis is concerned with serial data transmission at 9600 bit/sec over a voiceband channel, where the main impairments are additive noise and intersymbol interference, and the latter varles slowly with time. The thesis includes a brief description of the ionospheric propagation medium and presents an equivalent baseband model of the HF channel, suitable for computer simulation of quadrature amplitude modulation (QAM) systems. A study of 16-point QAM signals transmitted over voiceband HF channels is then carr-iod out usj-ng the given channel model. Several cost effective near-maximum-likelihood detection processes have been developed for HF modems. Each detector is here preceded by an adaptive linear filter that is adjusted to make the sampled impulse response of the channel and filter minimum phase. These detectors require an accurate knowledge of the sampled impulse response of the channel, if their full potential is to be achieved. The results of computer-simulation tests on the near-maximum-likelihood detectors are given, where these tests assume that other receiver operations such as channel estimation and adaptive linear filtering, together with element timing synchronisation and Doppler shift correction, are carried out perfectly. A recently developed HF channel estimator employing a simple feedforward transversal-filter and requiring knowledge of the number of skywaves is next investigated and a starting up procedure is developed for such an estimator. The technique is then made fully adaptive in the sense that it continues to operate correctly when the number of skywaves changes. Results of computer simulation tests are then presented showing the performance of the above detectors when operating with a channel estimator and adaptive linear filtering. Finally modem synchronisation is studied and various techniques of element timing and carrier frequency synchronisation are proposed.