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The investigation of the Faraday eeect in DyVO 4-type Jahn-Teller crystals, containing two Kramers doublets E 0 and E 00 in the low-energy part of the electron spectrum, is performed. The components of the tensor of linear magnetooptical eeect are obtained in the mean eld approximation. The ionic contributions into the eeect are separated, the features of their temperature dependencies are studied. The estimate of the so-called crystalline contributions into the Faraday eeect is performed. It is shown that the crystalline contributions increase and can be of the same order as the ionic one when we approach to the absorption edge. One of the most topical problems of physics is the investigation of the structural phase transitions (SPT) which are interesting both theoretically and from the point of view of searching for the new physical eeects promising in their practical use. The investigators attention is increasingly drawn by the SPT in which Jahn-Teller eeect is evident. Such transitions are observed, particularly in the rare-earth vanadate crystals. The change of the lattice symmetry in the crystals of this type is accompanied by the homogeneous deformation and considerable restructuring of the electron subsystem which results, as a rule, in the anomalies of their elastic, magnetic and optical properties 1{4]. The microscopic theory of the magnetooptical eeect in dielectric ionic crystals was developed in 5,6]. The methods suggested in them is used in this paper to investigate the Faraday eeect in Jahn-Teller crystals of the DyVO 4 type with Kramers rare-earth ions. The linear magnetooptical eeect is described by the component of the tensor of dielectric permeability proportional to the external magnetic eld ~ H. For tensor " (!) as a starting we assume the expression in terms of the two time retarding Green functions hh ^

MAGNETOOPTICAL EFFECT IN JAHN-TELLER CRYSTALS WITH KRAMERS RARE-EARTH IONS