  We extend the duality symmetry between the electric and the magnetic fields
to the case in which an additional axion-like term is present, and we derive
the set of Maxwell's equations that preserves this symmetry. This new set of
equations allows for a gauge symmetry extending the ordinary symmetry in the
classical electrodynamics. We obtain explicit solutions for the new set of
equations in the absence of external sources, and we discuss the implications
of a new internal symmetry between the axion field and the electromagnetic
gauge potential.
