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On-body transmission represents a challenge due to human body shadowing. This paper proposes a Sommerfeld-Goubau single-wire transmission line (SWTL) implemented using electronic textiles for low-loss on-body links up to millimeter-wave frequencies, overcoming the spherical spreading loss and on-body absorption. The SWTL is fabricated using a conductive thread suitable for embroidery on textiles. A compact tapered launcher is implemented on a flexible polyimide substrate to excite the surface mode along the SWTL. In space, a 3 m-long line maintains a forward transmission over &#x2212;10 dB between 1 and 3 GHz. The SWTL link is characterized for different body parts showing under 20 dB insertion loss with a 1 cm air gap. Across the torso, a forward transmission over &#x2212;20 dB is maintained from 0.5 to 2.5 GHz, which represents at least 20 dB improvement over two antennas, of larger dimensions, over-the-air. Directly on-skin, the SWTL can be used around 1 GHz with an <inline-formula> <tex-math notation="LaTeX">$S_{21}$ </tex-math></inline-formula> over &#x2212;25 dB, over 50 dB improvement over two on-skin antennas. At 50 GHz, the shielded SWTL exhibits an ultra-low on-body attenuation around 0.11 dB/mm, a four-fold improvement over a microstrip line on the same substrate. It is concluded that SWTLs can enable ultra high-speed future body area networks.