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At frequencies above the maximum usable frequency for ground-to-ground ionospheric communication, propagation is possible between terminals located in the ionosphere. This phenomenon has been studied in the past by use of the ray theory and is treated in this paper by use of the mode theory. At a given HF frequency there are a number of modes that are well trapped and a number that leak profusely to the topside of the ionosphere. As the frequency is increased, the number of well trapped modes decreases. Ultimately, only one mode is reasonably well trapped and leakage even of this mode finally sets in. The frequency at which this happens determines the maximum usable frequency of the ionosphere for whispering-gallery propagation. By use of a Chapman model of ionospheric density, this frequency is calculated to be about six times the vertical penetration frequency for the F region. Mode theory shows that the whispering gallery associated with the F region can be used to explain both round-the-world echoes and long distance satellite observations.