Аннотация:We found the spin integral of motion for neutrinos propagating in moving and polarized matter. Contraryto all previous studies this is the exact spin operator commuting with the Hamiltonian for a neutrino in matter whichmoves in an arbitrary direction relative to the direction ofneutrino propagation. The operator obtained opens up thepossibility of consistent classification of neutrino states insuch a medium and, as a consequence, a systematic description of the related physical phenomena. Using the operator,we obtain a dispersion relation for neutrinos in arbitrary moving matter and consider its particular cases.