A general, relativistically exact formulation of scattering of electromagnetic waves by two or more objects in relative, uniform motion is presented. Coupled and separated integral equations are obtained for far-field scattering amplitudes of bodies within a system in terms of known far-field scattering amplitudes of the isolated obstacles. The integral equations are accessible for iteration analogous with the case of nonmoving objects. Explicit expressions and numerical results are given for the two-dimensional problem of two parallel, perfectly conducting cylinders.