  The lagrangian of the Kaluza-Klein theory, in its simplest five-dimensional
version, should include not only the scalar curvature R, but also the quadratic
Gauss-Bonnet invariant. The general lagrangian is computed and the resulting
non-linear equations which generalize Maxwell's system in a quite unique way
are investigated. The possibility of the existence of static solutions is
presented, and the qualitative behaviour of such solutions is discussed.
