Singularities in general relativity coupled to nonlinear electrodynamics

We study here some consequences of the nonlinearities of the electromagnetic field acting as a source of Einstein's equations on the propagation of photons. We restrict to the particular case of a ``regular black hole'', and show that there exist singularities in the effective geometry. These singularities may be hidden behind a horizon or naked, according to the value of a parameter. Some unusual properties of this solution are also analyzed.