Multilayer structures with short periods have been systematically investigated using a tunable soft X-ray synchrotron, BESSY II, and X-ray tube radiation. Multilayer X-ray mirrors of W/B(4)C, W/Sc, Mo/B(4)C, Mo/C, La/B(4)C, Cr/C and Cr/Sc, with periods from 0.8 nm to 3.5 nm and number of periods up to 300-400, were constructed and investigated. The high reflectivity and spectral resolution of the mirrors allow them to be used to create multimirror systems for X-ray diagnostics of high-temperature plasma, for X-ray astronomy and microscopy.