For cubic lime-stabilized and yttria-stabilized zirconia ceramic alloys the temperatures at which the onset of metastability and a sharp reduction in ionic conductivity occur are observed to coincide, appearing at approximately 1000 degrees C and 650 degrees C respectively. This behavior is attributed to the development of quadrupolar (orientational) glass states in each alloy below its transition temperature. We suggest that several other unexplained phenomena including tetragonal distortion in these cubic phases may also be understood by reference to the alloys' crystalline structures, which differ slightly. At equilibrium, each possesses a random two-component crystalline constitution, one component of which is a low-symmetry quadrupole intergrown with the other and capable of switching its unique axis in a small number of different directions. The quadrupoles interact, thereby imparting a disordered stress on the other component in the lattice. Such a structure is identifiable as a quadrupolar glass, the elastic analog of a spin glass.