A semianalytical study of the diffusiophoretic motion of a finite string of dielectric spheres in a solution of symmetric electrolyte with a constant concentration gradient along the line through their centers is presented. The spheres may differ in radius and in zeta potential, and they are allowed to be unequally spaced. Also, the spheres can be either freely suspended in the fluid or linked by infinitesimally thin rods. The thickness of the electrical double layers surrounding the particles is assumed to be small relative to the radius of each particle and to the gap width between any two neighboring particles, but the effect of the polarization of the mobile ions in the diffuse layer is taken into account. A slip velocity of fluid and normal fluxes of solute ions at the outer edge of the thin double layer are used as the boundary conditions for the fluid domain outside the diffuse layer. Using a collocation method along with these boundary conditions, a set of electrokinetic governing equations is solved in the quasisteady state situation and the particle interaction effects are calculated for various cases. It is found that particles with the same zeta potential will interact with one another, unlike the no-interaction results obtained in previous investigations assuming that the double layer is infinitesimally thin. For most situations, the particle interaction among the spheres is a complicated function of the properties of the spheres and ions, and it no longer varies monotonically with the extent of separation for some cases. No general rule can make an adequate prediction for such complicated phenomena.