The electrophoretic motion of two freely-suspended, non-conducting arbitrary coaxial prolate particles of revolution with thin electrical double layers is investigated using the method of internal distribution of singularities. Corrections to the Smoluchowski equation due to particle interactions are determined. The electrophoretic mobilities of two prolate spheroid particles are calculated for different distances of two particles, various ratios of zeta potentials and a variety of parameters of particle shape. It is also found that the electrophoretic particles in our problem do not interact with one another when they have equal surface zeta potentials.