  The evolution of coupled fermions interacting with external axial-vector
fields is described with help of the classical field theory. We formulate the
initial conditions problem for the system of two coupled fermions in
(3+1)-dimensional space-time. This problem is solved using the perturbation
theory. We obtain in the explicit form the expressions for the leading and next
to the leading order terms in the expansion over the strength of external
fields. It is shown that in the relativistic limit the intensity of the fermion
field coincides with the transition probability in the two neutrinos system
interacting with moving and polarized matter.
