  We establish a new self-consistent system of equations accounting for a
nonminimal coupling of the cooperative gravitational, electromagnetic and
pseudoscalar (axion) fields in a multi-component relativistic plasma. The
axionic extension of the nonminimal Einstein-Maxwell-Vlasov theory is based on
two consistent procedures. First, we use the Lagrange formalism to obtain
nonminimal equations for the gravitational, electromagnetic and pseudoscalar
fields with the additional sources generated in plasma. Second, we use the
Vlasov version of the relativistic kinetic theory of the plasma, guided by the
cooperative macroscopic electromagnetic, gravitational and axionic fields, to
describe adequately the response of the plasma on the variations of these
fields. In order to show the self-consistency of this approach we check
directly the compatibility conditions for the master equations for the
cooperative fields. Using these compatibility conditions we reconstruct the
ponderomotive force, which acts on the plasma particles, and discuss the
necessary conditions for existence of the distribution function of the
equilibrium type.
