  We establish a new self-consistent system of equations for the gravitational
and electromagnetic fields. The procedure is based on a non-minimal non-linear
extension of the standard Einstein-Hilbert-Maxwell action. General properties
of a three-parameter family of non-minimal linear models are discussed. In
addition, we show explicitly, that a static spherically symmetric charged
object can be described by a non-minimal model, second order in the derivatives
of the metric, when the susceptibility tensor is proportional to the
double-dual Riemann tensor
