We study the scattering of a non-Abelian dyon and photons. We demonstrate t
hat two photons are necessary for Compton scattering of a non-Abelian dyon,
through S-matrix expansion. One of these two photons is associated with el
ectric four-potential and is ordinary, while the other is associated with m
agnetic four-potential and is highly energetic and responsible for scatteri
ng of magnetic charge of the non-Abelian dyon. We also study dyon-photon, d
yon-dyon, and dyon-antidyon scattering and the self-energy of the dyon and
both photons in non-Abelian gauge theories.