By use of small angle and ultra small angle neutron scattering techniques it was established that amorphous xerogels of hydrous zirconia and hafnia possess fractal properties in a wide range of scales, and the fractal dimension of these materials can be intentionally modified by changing their precipitation pH. It was found that the changes in fractal dimension and specific surface area of hydrous zirconia and hafnia xerogels are governed by the changes in the adsorption of anions onto their surface. It was demonstrated that particle size and specific surface area of ZrO₂ and HfO₂ nanopowders prepared by thermal decomposition of hydrous zirconia and hafnia xerogels depends strongly on the mesostructure and synthesis conditions of these xerogels.