The electronic structures of oxygen vacancies and substitutional divalent and trivalent cobalt ions in cubic yttria stablilized zirconia crystals were calculated by the discrete-variation-al (DV)-Xα method. Various clusters account for different configurations of the oxygen vacancies and different coordinations of the cobalt ions. The oneelecton eigenvalues and charge distributions of the clusters were given. The energies of optical transitions were obtained by transition-state calculations, and compared with available experimental date. The effects of composition and thermal processing on the absoption spectra of the crystal are discussed.