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The waveguide properties of annular-shaped plasma columns in the absence of an external magnetic field are investigated. The analysis of the structure shows several novel characteristics of the propagation system. The modes of propagation on an annular plasma column are surface-wave modes, one on the inner surface and one on the outer surface. The dispersion relations obtained from the field analysis is plotted, and it is shown that the inner surface wave is a backward wave. When a conducting cylinder is placed on one surface of the annulus one obtains single-mode solutions, since the other mode is shorted out by the conductor. It is shown that the surface waves in the presence of a conducting boundary also exhibit pronounced backward-wave characteristics. The dispersion curves for these propagation systems are plotted.