  We study the evolution of two mixed Dirac neutrinos in an external
axial-vector field. The dynamics of this system is described in the framework
of relativistic wave equations approach on the basis of the known solutions of
the Dirac equation in an external field with a given initial condition. The
general solution of the initial condition problem, exactly accounting for the
external field, is obtained. Then we consider special form of the external
field which corresponds to the standard model neutrino interactions with the
background matter. In this limit we derive the transition probability and
compare it with the previously known results.
