Host matrices for actinides prepared by self-propagating high-temperature synthesis are studied. The matrices consist of a pyrochlore or fluorite phase and metallic molybdenum. The factor determining the structural type of the crystal lattice of the target phase is the ionic radius ratio. When the difference in the ionic radii is insignificant, as in the case of Y3+ (r 0.102 nm) and Zr4+ (r 0.084 nm), the oxide Zr1-xYxO2-0.5x with a fluorite structure is formed, in which the cations occupy the eight-coordinate sites. This structure permits incorporation of heavy lanthanides and tetravalent actinides: U4+ (r 0.10 nm), Np4+ (r 0.098 nm), and Pu4+ (r 0.096 nm). When the difference in the ionic radii is more considerable, as in the case of Y3+ and Ti4+ (r 0.061 nm), a pyrochlore-related structure is realized. In this case the cations occupy different (eight- or six-coordinate) sites. The pyrochlore structure is preserved if the radii of ions occupying different structural sites change in parallel. This structure is typical of zirconates of trivalent actinides and light REEs. The decision on the major host phase for actinides is determined by the waste composition. At low content of light REEs and americium an oxide with a fluorite-related structure shows promise. At high content of these elements, zirconates and titanates with the pyrochlore structure are more stable.