A relativistic formulation for the fields of sources in a uniformly moving, isotropic, dispersionless, conducting medium is developed in terms of Green's functions. Solutions are found in closed form for the cases of stationary charge sources and harmonic current sources. Cerenkov phenomena are observed and discussed. The work differs from former treatments in that a self-consistent scheme is given which accounts for relaxation effects involving conduction charges. The results apply for all values of conductivity.