Cubic oxides with pyrochlore and garnet structures are promising matrices for long-lived actinides immobilization. Their isomorphic capacity with respect to An and REE was determined. To predict the long-term behavior of these matrices under their underground disposal radiation stability of synthetic pyrochlores and garnets was studied. Most of titanate phases have the critical (amorphization) doses close to 0.2 displacements per atom at 298 K. This value is significantly higher for Sn- and Zr-rich pyrochlores. Corrosion behavior of the pyrochlore- and garnet-composed matrices was investigated. The lowest actinides leach rates were observed in water and alkaline solutions most typical for underground waste repositories. Amorphization of the phases has a low influence on their corrosion behavior in solutions. Possibility for joint incorporation of actinides and Tc into zirconate- and titanate-based matrices with the pyrochlore structure is discussed.