The electrophoretic mobilities of two spherical particles are analysed for the case where the electrical double layer is no longer thin with respect to the particle sizes, but the zeta potentials on the particles are low. Using a method of reflections, we obtain the mobilities as a power series in 1/r(12) up to O(r(12)(-10)) (where r(12) is the center-to-center separation of the spheres), with the proviso that the double layers on the two particles do not overlap. Unlike the case of thin double layers, there is now a nonzero interaction between identical particles. The first term in the interaction is O(r(12)(-3)), but the coefficient becomes large for thick double layers. An expression for the average mobility of a mildly polydisperse suspension of spheres with thick double layers is then derived correct to first order in the volume fraction of the spheres. The results of the reflection calculation are then used to obtain an approximate evaluation of this expression. It is found that the first order effect for thick double layers is significantly larger than it is for thin double layers, and that the average effect of polydispersity in size or surface potential is weak unless the double layers are quite thick. For a monodisperse suspension, an expression is obtained for the mean square deviation of the particle velocity from the mean velocity. An approximate evaluation of this expression using the reflection results shows that the magnitude of the mean square fluctuations in the direction of the applied field can be significantly larger than that in the transverse direction.