X-ray multilayer supermirrors for the energy range up to 20 keV have been theoretically studied and experimentally measured with synchrotron radiation. A multilayer mirror with 50 W/Si bilayers with different thicknesses on the Si substrate has a smooth reflectivity of up to 32% in the whole energy range from 5 to 22 keV at a grazing incidence angle of 0.32 degrees which is considerably larger than using total external reflection. (C) 1995 American Institute of Physics.