The research methods and the first results obtained in the study of the roughness of single-crystal silicon (111) substrates processed at the final stage by various methods are described: traditional polishing without the use of chemical-mechanical polishing (CMP), with the use of CMP and without CMP, but with the use of oxide cerium nanopowders. The efficiency of using CeO2 nanopowders has been demonstrated. The following effective roughness values were obtained: without CMP - 3.56 nm, with CMP - 0.54 nm, and without CMP, but with CeO2 polishing - 0.93 nm. Keywords: Surface, roughness, X-ray optics, deep grinding-polishing.