The structural transformations (processes of hydroxylation-dehydroxylation of a solid matrix, the formation of bonded water of different forms, morphological rearrangements, and the process of crystallization) in amorphous or weakly crystalline samples of silica and alumina have been studied during their thermovaporous treatment in an autoclave at supercritical conditions in the presence of activating microadditives. The influence of the additives on the mechanism and kinetics of such processes is discussed. On the basis of these data for solid-phase crystallization, new ecologically pure fine-crystalline powder materials, which are widely used in industry [quartz (alpha-SiO2(q)) and corundum (alpha-Al2O3)], have been developed.