The possibilities are presented of X-ray diffraction methods for studying the propagation of surface acoustic waves (SAWs) in solids, including diffraction under total external reflection conditions and Bragg diffraction, using acoustically modulated X-ray multilayer mirrors and crystals. SAW propagation was studied using both meridional and sagittal diffraction geometries where the SAW wavevectors and X-ray photons are collinear or perpendicular, respectively. SAW propagation in a crystal leads to sinusoidal modulation of the crystal lattice and the appearance of diffraction satellites on the rocking curve. The intensities and angular positions of these diffraction satellites are determined by the SAW wavelength, amplitude and attenuation. Therefore, diffraction methods allow the analysis of the SAW propagation process and determination of SAW parameters. The influence of X-ray energy on diffraction by acoustically modulated crystals is studied for the first time. It is shown that changes in the X-ray energy can change the angular region where diffraction satellites exist under conditions of total external reflection. By contrast, in the Bragg diffraction region changes in the X-ray photon energy lead to changes in the X-ray penetration depth into the crystal and redistribution of the diffracted intensity among diffraction satellites, but do not change the angular divergence between diffraction satellites on the rocking curve. It is also shown that, in X-ray diffraction on acoustically modulated crystals on a number of successive reflections, a decrease in interplanar spacing leads to an increase in the number of diffraction satellites and a redistribution of diffracted radiation between them.