A rigorously posed electrodynamical problem of diffraction of a plane wave by a multielement diffraction grating that consists of cylindrical screens with arbitrary curvature is solved by the method of integral equations. We construct an integral representation of the Green function of the problem under consideration which gives a significant increase in the accuracy of calculations and investigate the phenomenon of resonance propagation of an electromagnetic wave along the axis of a two-layer grating irradiated with aE-polarized wave which propagates along the normal to the grating.