The search for high-temperature nuclear fuels is based on obtaining melting-point data from binary and ternary phase relationships. Arguments are presented that properties of important high-temperature materials used in nuclear fuels and fuel-element protective coatings have been obtained from nonequilibrium-phase diagrams and that the materials themselves are thermodynamically unstable. These data are time dependent and should be used with caution. Multicomponent solids at high temperatures have defect-stabilized equilibrium structures that can exhibit large deviations from stoichiometry. The properties of these materials are consistent with the view that the compound acts as a solvent for the individual constituents whose activities are dependent on the overall composition of the solid solution and on the environment when the environment includes a gas containing one or more of the constituents in the solid. At high temperatures, almost all stoichiometric refractory carbides and nitrides are unstable and evaporate in-congruently. In closed systems, incongruently evaporating materials eventually achieve stable configurations that are inherently mass dependent and geometry dependent. These mass-dependent, geometry-dependent properties include melting temperatures. Many nonequilibrium stoichiometric compounds yield apparent melting points when heated rapidly while exhibiting incongruent vaporization hundreds of degrees below the reported melting points. Experiments show that the composition of nonstoichiometric single phase solids that are in equilibrium with the same vapor composition can differ from the nonequilibrium time-dependent stoichiometric melting compositions by >50%. Equilibrium compositions of nonstoichiometric nuclear fuels and fuel coatings are temperature dependent. The materials exhibit a wide range of evaporation rates at high temperatures. They undergo time-dependent compositional and structural changes when subjected to temperature cycles and temperature gradients. Such changes can lead to complex reactivity differences in gas environments and the development of time-varying internal stresses that are position dependent and composition dependent. Such effects limit the performance of high-temperature fuels. Understanding the theoretical causes of these effects is important in their minimization. Minimization of the effects is important in reducing the degradation rates of both nuclear fuels and protective coatings.