The two-dimensional problem of horizontally polarized wave scattering from an air-ground interface is considered. The diffraction problem is formulated by means of the extinction theorem, leading to a system of two simultaneous surface integral equations. Three perturbation techniques, namely the small-perturbation method, the phase perturbation method, and the small-slope approximation, have been applied to this system. Iterative relations for the terms of arbitrary order are obtained for each perturbation series. For the sinusoidal surface a benchmark solution, which remains stable near the points of Wood's anomalies, is developed. It is used to establish the area of validity of each perturbation technique by means of numerical comparison. ¿ 2000 American Geophysical Union