  In this paper we define a causal Lorentz covariant noncommutative (NC)
classical Electrodynamics. We obtain an explicit realization of the NC theory
by solving perturbatively the Seiberg-Witten map. The action is polynomial in
the field strenght $F$, allowing to preserve both causality and Lorentz
covariance. The general structure of the Lagrangian is studied, to all orders
in the perturbative expansion in the NC parameter $\theta$. We show that
monochromatic plane waves are solutions of the equations of motion to all
orders. An iterative method has been developed to solve the equations of motion
and has been applied to the study of the corrections to the superposition law
and to the Coulomb law.
