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Аннотация The classes of one-dimensional nonlinear evolution equations of the third order, which solutions are interconnected by generalized Miura and Backlund trunsformations, are obtained. The research is based on construction of Lax pairs by Calogero (J.Math.Phys. 32 (1991)(1) 72–74). It is proved that arbitrary one-dimensional nonlinear evolution equations, which can be presented in the form of local conservation law, admits a bunch (non-enumerable set) of Lax pairs by Calogero depended on several spectral parameters