The characteristics of the discrete propagation modes on horizontal thin-wire structures located above a dissipative earth are investigated. In addition to the well-known transmission line mode, a new root of the characteristic equation is found which is identified as a “surface-attached” mode because of its close connection with the Sommerfeld pole (Zenneck wave) in some parameter ranges. Under many conditions the surface-attached mode suffers substantially less attenuation along the propagation direction than does the transmission line mode. Numerical investigation of the propagation constants of the two modes is made, and field plots for the modes for a variety of wire parameters are presented.