  We develop the idea of local duality symmetry (LDS) in gauge field theories.
Using Clifford algebra techniques we construct dually invariant scalar
Lagrangian of electrodynamics in the presence of sources and demonstrate that
in tensor formalism it is exactly the same as the usual one. Then we localize
the duality symmetry with two possible options for the appearing pseudovector
field - massive and massless. The first option might be interpreted as a
candidate for dark matter. Perspectives of the application of LDS in QCD are
briefly discussed.
