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In the present work, the problem of plane wave diffraction by a wedge with an anisotropic impedances is investigated for the case of almost grazing incidence. Wedge is a canonic structure and diffraction from wedge may be used in modelling scattering from a variety of complex structures. The closed form solution is given for functional equations. The obtained analytic expression for the spectral functions is substituted to the Sommerfeld integrals, which are evaluated by means of steepest descent technique.Then, the analytical expressions for the diffraction coefficient for both magnetic and electric field components are derived.