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In this contribution we report on the theoretical study of basic vacancy-like defects in cubic zirconia and yttria stabilized zirconia. In particular, we concentrate on oxygen vacancy, zirconium vacancy and oxygen vacancy – yttrium complex. Relaxed atomic configurations of studied defects are obtained by means of an ab initio pseudopotential method within the supercell approach. Positron characteristics, like positron lifetime and binding energy to defects, are calculated using self-consistent electron densities and potentials taken from ab initio calculations.