The explanation for the apparent superluminal motions seen in the cores of some quasars is easily accounted for by special relativity. Because the activity occurs in a local region of space-time near the quasar, it is not necessary to worry about the cosmological red shift affect which accounts for the relative motion of the entire quasar with respect to the Milky Way. The superluminal motions are due to the close to the speed of light motions of plasma clouds ejected by the quasar very close to our line of sight. The same relativistic explanation would work for any quasar regardless of its distance.