Possible reasons for the temperature hysteresis of the Hall and diagonal components of resistivity tensor in tritellurides and tetratellurides of rare-earth metals, respectively, are analyzed. The width of this hysteresis exceeds 100 K in both families. This hysteresis is related to the charge density wave (CDW), but its detailed nature is still being discussed. It is known that it cannot be explained by a temperature variation in the CDW wave vector. In this paper, we discuss various interpretations of the observed hysteresis, present new experimental data showing a strong dependence of the hysteresis value on the temperature range, and propose new experiments (or a detailed analysis of unpublished data from existing ARPES measurements) that can substantiate or refute the proposed explanations for this unusual effect.