  We study nonlinear vacuum electrodynamics in the first-order formulation
proposed by Pleba\'nski. We analyze in detail the equations of motion, and
identify conditions for which a singularity can occur for the time derivative
of one of the field components. The resulting degenerate behavior can give rise
to a shock wave with a reduction of the local number of degrees of freedom. We
use an example model to illustrate the occurrence of superluminal propagation
for field values approaching the singularity.
