Crystalline phases of pyrochlore (e.g., CaPuTizOT, CaUTi207) have been proposed as a durable ceramic waste form for disposal of high level radioactive wastes including surplus weapons-usable plutonium. In this paper, we use a linear free energy relationship to predict the Gibbs free energies of formation of pyrochlore phases (CaMTizOT). The Pu-pyrochlore phase is predicted to be stable with respect to PU02, CaTiO~, and Ti02 at room temperatures. Pu-pyrochlore is expected to be stable in a geologic repository where silica and carbonate components are absent or limited. We suggest that a repository in a salt formation be an ideal environment for disposal of high level, pyrochlore-based ceramic wastes. In such environment, adding CaO as a backfill will make pyrochlore minerals thermodynamically stable and therefore effectively prevent actinide release from these mineral phases.