A theoretical description of bistable donors in polar semiconductors is proposed. The donor states are described within the one-band approximation, which takes into account a finite width and nonparabolicity of the conduction band. The interaction between the defect and the crystal 1attice is assumed in the Fröhlich form. For the bistable indium impurity in cadmium fluoride, a coexistence of strongly and weakly localized donor states has been obtained. The calculated energies for both the states and absorption band shape in the 3-eV range are in agreement with experiment.PACS numbers: 71.55.-i Optical absorption spectra of cadmium fluoride crystals doped with indium exhibit unusual properties [1,2,3]. In these crystals, the two asymmetric absorption bands are observed [2,3] with the maxima at 0.2 eV and 3 eV, respectively. The sample cooled in darkness shows in low temperatures the 3-eV band only, while the sample illuminated with the white light starts to absorb the infrared (IR) radiation in the 0.2-eV band. During the illumination, the IR absorption increases, while the absorption in the visible and ultraviolet range decreases. The threshold for the visible absorption is determined to be 1.9 eV [2] and the thermal activation energy for the Hall effect is 0.25 eV [2]. The difference between these values, i.e. 1.65 eV, is the Stokes shift. These results lead to the conclusion [2,3] that the indium impurity in CdF 2 is a bistable donor which possesses two sets of quantum states with energy levels in a gap: strongly localized states, which are responsible for the absorption in the 3-eV range, and weakly localized shallow states, which are responsible for the absorption in the 0.2-eV range. This interpretation has been confirmed by the results of theoretical investigations [4,5]. In the present paper, the theory [4,5] is extended by taking into account a finite width of the conduction band, performing all the calculations in the k-space with the Debye