  We study an electrodynamics consistent with anisotropic transformations of
space-time with an arbitrary dynamic exponent $z$. The equations of motion and
conserved quantities are explicitly obtained. We show that the propagator of
this theory can be regarded as a quantum correction to the usual propagator.
Moreover we obtain that both the momentum and angular momentum are not
modified, but their conservation laws do change. We also show that in this
theory the speed of light and the electric charge are modified with $z$. The
magnetic monopole in this electrodynamics and its duality transformations are
also investigated. For that we found that there exists a dual electrodynamics,
with higher derivatives in the electric field, invariant under the same
anisotropic transformations.
