The formation of nano-size ceramic fibers having diameters as small as 20 nm is described. This material was obtained by a simple precipitation reaction from a supercritical aqueous dysprosium bromide solution at high temperatures (450 degrees C). The nano-structures have unusually high structural stability for extended time periods in this extreme solvent environment. The experimental procedures are described and analysis of the materials by scanning and transition electron microscopy, and x-ray diffraction is presented. The new materials may have useful applications as high-strength, corrosion resistant materials or as stable catalyst supports for extreme conditions.