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The effect of Sr-nonstoichiometry on phase composition, microstructure, defect chemistry and electrical conductivity of SrxZrO3−δ and SrxZr0.95Y0.05O3−δ ceramics (SZx and SZYx, respectively; x = 0.94–1.02) was investigated via X-ray diffraction, scanning electron microscopy, energy-dispersive X-ray spectroscopy and impedance spectroscopy followed by distribution of relaxation times analysis of impedance data. It was shown that at low Sr deficiency (x > 0.96 and 0.98 for SZx and SZYx, respectively) a solid solution of strontium vacancies in strontium zirconate crystal structure forms, whereas at higher Sr deficiency the secondary phase, zirconium oxide or yttrium zirconium oxide, is precipitated. Yttrium solubility limit in strontium zirconate was found to be close to 2 mol%. Y-doped strontium zirconates possess up to two orders of magnitude higher total conductivity than SZx samples. A-site nonstoichiometry was shown to have a significant effect on the electrical conductivity of SZx and SZYx. The highest total and bulk conductivity were observed at x = 0.98 for both systems. Increasing the conductivity with a rise in humidity indicates that proton conduction appears in the oxides in wet conditions. A defect model based on consideration of different types of point defects, such as strontium vacancies, substitutional defects and oxygen vacancies, and assumption of Y ions partitioning over Zr and Sr sites was elaborated. The proposed model consistently describes the obtained data on conductivity.