  We generalise the electric-magnetic duality in standard Maxwell theory to its
non-commutative version. Both space-space and space-time non-commutativity are
necessary. The duality symmetry is then extended to a general class of
non-commutative gauge theories that goes beyond non-commutative
electrodynamics. As an application of this symmetry, plane wave solutions are
analysed. Dispersion relations following from these solutions show that general
non-commutative gauge theories other than electrodynamics admits two waves with
distinct polarisations propagating at different velocities in the same
direction.
