A system consisting of an equilibrium medium formed by charged particles and electromagnetic field is considered in the classical case at weak interaction between subsystems. The field is described with all the statistical moments of electric and magnetic fields. The moments are reduced description parameters of the herein developed theory based on the Bogolyubov reduced description method of nonequilibrium states. The generalized Bogolyubov condition of the complete correlation weakening between the subsystems is used as a boundary condition to the Liouville equation. Distribution function of the system is calculated up to the third order in electromagnetic interaction. Time equations for the reduced description parameters are written in a compact form using a generating functional for the field moments and a generating functional for field correlations (centered moments, fluctuations). The obtained equations generalize the nonlinear electrodynamics in equilibrium media for the case of fluctuations of electromagnetic field being taken into account.