Maxwell's equations are generalized for conducting media moving relative to inertial frames with electromagnetic substratum flow. It is shown that the resultant electromagnetic field equations for moving conducting media are Galilei covariant. The theory is of interest for the electrodynamics of such conducting media as plasmas, solid conductors, conducting macroparticles, etc. These systems can presently be accelerated to velocities up to υ ∼ 104 to 105 m/s, which are small in comparison with the velocity of light, υ ≪ c0 = 3 × 108 m/s.