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A review is presented of the problems inherent in transmitting data over h.f. links. The propagation medium imposes characteristics of time and frequency dispersion, fading and delay distortion upon the transmitted signal, particularly when wide bandwidths are used. The magnitude and variability of these features are quantified and a simplified expression for the received signal is derived. Techniques that have been used to transmit high data rates over h.f. links are summarized and their relative merits compared. It is concluded that the ionosphere continues to be a limiting factor in the design of an efficient modem, but that recent developments in microelectronics provide the potential to make a significant improvement in the performance of future communication systems.