The parameters of radiation sensitivity of the oxygen-doped fluorite crystals were calculated in a onedimensional model. The limit concentrations of the color centers as a function of the concentration of the oxygen impurity in the fluorite crystal were defined. Fluorite crystals with anti-Frenkel defects in the anion sublattice of the crystal have a specific property: the discolored after irradiation crystal being irradiated repeatedly with ionizing radiation retains the "memory" of the preceding irradiation. Using an ion chain model this paper studies under what conditions the "radiation memory" effect can arise in the MeF2-O 2− crystals as well as the extent of its contribution into the overall radiation sensitivity of the crystal.