Abstract <p>A dynamic theory of coherent X-ray radiation generated by a beam of relativistic electrons in a composite target “amorphous layer-vacuum-periodic layered medium” has been developed. A periodic layered medium consists of three different layers arranged periodically, with the layers located at an arbitrary angle to the target surface. Coherent X-ray radiation exits through the rear surface of the target; that is, radiation in the periodic layered medium occurs in the Laue scattering geometry. Within the framework of the two-wave approximation of the dynamic theory of diffraction, expressions describing the spectral-angular densities of parametric X-ray radiation (PXR) in the periodic layered medium and diffracted transition radiation (DTR) are obtained and studied.</p>