The EPR spectrum temperature dependence of Tl²⁺(II) paramagnetic centers in Rb₂SO₄, Cs₂SO₄ crystals have been investigated. At 100K>T>40K the local symmetry of Tl²⁺(II) paramagnetic centers is C₂. The broadening and doubling of EPR spectrum lines with decreasing of T<40K were observed. The angular dependence of lines positions indicate that two structural nonequivalent positions of Tl²⁺(II) paramagnetic center exist at T<20K. The measurement of dielectric constant of crystals displayed the absence of phase transition in this temperature range. The transformation of EPR spectrum is explained by motion ofTl²⁺(II) paramagnetic center between two structural nonequivalent states arising near noncentral positions. Parameters of the potential have been extracted by fitting of the temperature dependence of EPR spectrum. Two nonequivalent states are possible due to large difference between ionic radius of Tl²⁺(II) and Rb⁺, Cs⁺.