The problems connected with the design of waveguides suitable for long-distance transmission are briefly analysed, and features peculiar to this transmission medium are contrasted with those of the more conventional kind.All known types of waveguides are discussed and their properties are analysed in detail; it is demonstrated conclusively that the only waveguides suitable for long-distance transmission are the dielectric-coated waveguide and the anisotropic waveguide, of which there are several distinct types. Design formulae for these are given and analysed at length.An extensive quantitative discussion of typical waveguide discontinuities is given, and the mechanism of mode conversion-reconversion, responsible in large measure for signal distortion, is explained. It is shown how to design suitable waveguides (dielectric coated or anisotropic) to counteract these effects successfully.The paper concludes with examples.