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Asymptotic method of calculation of electromagnetic waves diffraction from a radio- transparent layered structure (radome, antenna cover) is considered. This method is based on a combination of the beam representations and the expansions characteristic to the "boundary layers": beam series coefficients are given as the functions of the point in space extended along the normal direction. The problem has two small dimensionless parameters depending on the wavelength, curvatures of the boundary surfaces and the wave front, and the layer thickness. In this case, the analysis is done based on certain relations between the values of these parameters.