Two immiscible liquid phases form when an aqueous mixture of the electrically neutral polymers dextran and polyethylene glycol are equilibrated at sufficient concentrations. Certain supporting electrolytes which contain sulphate, phosphate or citrate ions partition unequally between the phases, and in their presence, electrophoresis of a drop of one phase suspended in the other is observed, with large mobilities. These mobilities depend linearly on the radius of the drop and the direction of the drop's motion is reversed when the disperse phase and the continuous phase are interchanged. When those ions which produce electrophoresis are present the potential Implied by the direction of electrophoresis is opposite to the Donnan potential observed between the two phases. To explain these results, we postulate an electric dipole layer associated with a mixture of oriented polymer molecules at the surface of a drop. In addition, a potential difference between the interiors of the two phases results from the unequal ion distribution. For the idealised model of a surface layer of point dipoles the inner and outer diffuse layers carry net charges equal in magnitude but opposite in sign. The classical theory of electrophoresis due to Henry, Overbeek and Booth is adapted to the motion of an emulsion drop under an electric field when diffuse ionic layers are present inside and outside the drop. Relaxation effects are treated for the case where the two diffuse layer thicknesses are small compared with the drop radius. An expression is obtained for the electrophoretic mobility of a drop which depends linearly on radius and also shows an increase with increase in salt concentration. The theory presented here is related to the work of Levich.