Velocity of propagation of a signal, and the space-time metric in nonlinear electrodynamics

It is proved that, in nonlinear electrodynamics, the velocity of propagation of a small timedependent disturbance (which can be assumed to be a signal) in an external field depends on the strength of the field and can exceed the velocity of light in a vacuum. This implies that, in an external field, the order (in time) of the emission and reception of a signal can depend on the reference system if the usual Lorentz-transformation formula holds. The possibility is considered of avoiding this contradiction by the introduction of a space-time metric dependent on the field or by the introduction of a new selection principle permitting the exclusion of nonlinear Lagrangians which allow signal velocities greater than the velocity of light.