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The theory of propagating waves near a surface is reviewed with an eye to gain insight into the mechanisms involved, and to provide analytical-based models, for power-efficient on-body propagation. The Zenneck wave, and in particular the Norton wave, are appraised as candidate mechanisms for the propagation. For flush-mounted (ldquoband aidrdquo) antennas, desired for on-body sensors, the Norton wave is the only direct propagation mechanism between the sensors. The Norton wave fits very well to simulation results presented here, and comparisons are also made with available published physical experiments, although these measurements typically feature the optical paths of elevated, or non-flush, antennas.