  We study the evolution of mixed scalar as well as spinor fields within the
context of the classical field theory. The initial condition problem is solved
and the fields distributions, exactly accounting for the initial conditions,
are obtained for both scalar and spinor fields. In the system of two coupled
fields we consider the special case of the initial conditions which are rapidly
oscillating functions. It is demonstrated that the energy densities of the
scalar fields and the intensities of the spinor fields coincide with the usual
transition and survival probabilities of neutrino flavor oscillations in
vacuum.
