  In this paper we have obtained several new results concerning the X-boson,
which is being considered recently as one of the main candidate of the dark
matter particle content. The classical electrodynamics for the X-boson model
was explored to understand its propagation in space-time. The field equations
(Maxwell-type) and the corresponding wave equations were obtained. They
indicate the dispersion relations of both a massive and massless particles.
These results can be interpreted as a photon and the X-boson (with a mass of 17
MeV), respectively. The gauge symmetry and gauge transformations were
discussed. A full model diagonalization was introduced to obtain a Maxwell
sector added up to a Proca sector. After that, we have obtained the retarded
Green functions which yield the inhomogeneous solutions of the wave equations
for the X-boson fields. We have applied this solution to the charge point
motion, and we transformed the potential solution to a quadrature problem. In
particular, as an example, we have analyzed the point charge in a straight line
uniform motion, where the corresponding electromagnetic charge were calculated.
