Wireless body-area networks require low power data transfer between on-body nodes, and much has recently been published about propagation between on-body sensors. Most of these contributions have comprised physical experiments, and they cover both on-body and off-body paths. The measurements to date have not produced conclusive evidence of surface waves. For compact, power-efficient sensors, there is a need for high antenna efficiency and low transmit power. Using high frequencies allows physically small antennas, and to be unobtrusive, flush, "band aid" antenna profiles are preferred. For communications between flush antennas via a direct path, a surface wave is required. Moreover, surface waves can propagate around modest body contours. This motivates a look at the theory of propagating waves near a body surface. The Zenneck and Norton waves are revived. These were originally conceived for propagation along the ground over intercontinental distances, and here we look to them for distances of centimetres along a body surface.