The process of forming three-component nanocrystalline fibers and powders of zirconia, yttria and alumina is studied depending on the component ratio and heat treatment temperature. It has been found that in the investigated system at 500-600 degrees C a nanocrystalline triple solid solution is formed, which exists up to 1200 degrees C. Beyond the above temperature, the triple solid solution decomposes into individual components. Specific regularities of changes in the crystalline structure and size of nanograins of oxides of triple solid solutions in the ZrO2(Y2O3)-Al2O3 system are established depending on the composition and thermal action. The structure--crystallite size--physical-chemical property relationship is also considered. The proposed synthesis method enables preparing nanocrystalline fibers and powders with a high degree of dispersion and reactive activity, whose use in composite materials and ceramics improves their service properties.