Off--great circle HF propagation effects are a common feature of the northerly ionosphere (i.e., the subauroral trough region, the auroral zone, and the polar cap). In addition to their importance in radiolocation applications where deviations from the great circle path may result in significant triangulation errors, they are also important in two other respects: (1) In systems employing directional antennas pointed along the great circle path, the signal quality may be degraded at times when propagation is via off--great circle propagation modes; and (2) the off--great circle propagation mechanisms may result in propagation at times when the signal frequency exceeds the maximum usable frequency along the great circle path. A ray-tracing model covering the northerly ionosphere is described in this paper. The results obtained using the model are very reminiscent of the directional characteristics observed in various experimental measurement programs, and consequently, it is believed that the model may be employed to enable the nature of off--great circle propagation effects to be estimated for paths which were not subject to experimental investigation. Although it is not possible to predict individual off--great circle propagation events, it is possible to predict the periods during which large deviations are likely to occur and their magnitudes and directions.