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The characteristic equation is derived for the propagation of surface waves guided by a planar two-dimensional corrugated structure. This equation is solved numerically to obtain the propagation wave number as a function of the direction of propagation on the surface. The data obtained illustrate the anisotropic nature of the wave propagation. In addition, an isolated surface wave is found to exist with its propagation wave number in a ‘forbidden’ region of wave number space. The relevance of this wave to a transmission null in a phased array antenna is discussed.