The thermodynamies of phase transitions associated with Frenkel aniondisorder in CaF2−type superionic conductors is considered. The short-range order in the arrangement of vacancies in the main anion sublattice and of anions in the octahedral interstices is describedin a pairwise approximation (of the Bethe type) with allowance for intractions of is described in a pairwise appromean-field approximation and the Frenkel-pair formation entropoy phenomenologically, with retention of linear and quadratie terms in defect concentration. Genetically related first and second order and diffuse phase transitions may be realized within the model proposed. A satisfactory quantitative agreement is obtained between the theoretical temperature dependence of heat capacity and that observed experimentally for CaF2 type compounds on diffuse transition to superionic state. The reason is discussed why the classical theory of point defects cannot be applied to these systems over theentire transition range. [Russian Text Ignored].