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It is shown that the processes of neutrino oscillations in an external magnetic field can be consistently described in the framework of a new quantum field-theoretical approach. It is based on the Feynman diagram technique with a modified distance-dependent propagator, which takes into account the geometry of neutrino oscillation experiments. Processes of neutrino oscillations, where the neutrinos are detected through the weak charged-current interaction, have been studied and numerical calculations have been carried out for some specific examples. A possible application to the solar neutrino problem is discussed.