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We report the investigations of the ion migration polarization in the yttria stabilized zirconia (YSZ) thin films in the Metal-Oxide-Metal (MOM) and Metal-Oxide-Semiconductor (MOS) stacks due to the drift of the oxygen vacancies under the external bias voltage applied between the electrodes. The parameters characterizing the drift of the oxygen vacancies in YSZ such as the ion drift activation energy, mobile ion concentration, and the drift mobility have been determined in the temperature range 300–500 K. These data are important for deeper understanding of the fundamental mechanisms of the electroforming and resistive switching in the YSZ-based MOM and MOS stacks, which are promising for the Resistive Random Access Memory (RRAM) and other memristor device applications.