  Within the scope of a Bianchi type-I (BI) cosmological model we study the
interacting system of spinor and electromagnetic fields and its role in the
evolution of the Universe. In some earlier studies it was found that in case of
a pure spinor field the presence of nontrivial non-diagonal components of EMT
leads to some severe restrictions both on the spacetime geometry and/or spinor
field itself, whereas in case of electromagnetic field with induced
nonlinearity such components impose severe restrictions on metric functions and
the components of the vector potential. It is shown that in case of interacting
spinor and electromagnetic fields restrictions are not as severe as in other
cases and in this case a nonlinear and massive spinor field with different
components of vector potential can survive in a general Bianchi type-I
spacetime.
