The ESR spectra of nanostructured samples of monoclinic ZrO2 irradiated by electrons with energies of 130 keV, 10 MeV, and by a beam of Xe ions (220 MeV) have been studied. It has been established that irradiation of samples with electrons (10 MeV) and ions leads to the formation of radiation-induced F+ centers in them. Thermal destruction of these centers is observed in the temperature range of 375–550 K for electron-irradiated and 500–700 K for ion-irradiated samples. It is shown that the decrease in the concentration of F+ centers is associated with the emptying of traps responsible for thermoluminescence (TL) peaks in the specified temperature range. In the samples irradiated with an ion beam, previously unidentified paramagnetic centers with g = 1.963 and 1.986 were found, the formation of which is likely to involve Zr3+ ions and oxygen vacancies. Thermal destruction of these centers occurs in the temperature range from 500 to 873 K.