The electrophoretic behavior of a spherical particle in a spherical cavity is analyzed theoretically, taking the effect of double layer polarization into account. We show that for the case where the particle is positively charged and the cavity uncharged if the surface potential of particle is high, the variation of the mobility of the particle as a function of kappa a has a minimum, kappa and a being respectively the reciprocal Debye length and particle radius. This minimum does not appear if the effect of double layer polarization is neglected. The variation of the mobility as a function of kappa a has a minimum for a medium value of lambda (= particle radius/cavity radius); it becomes negligible if lambda is either small or large. In the case where the particle is uncharged and the cavity positively charged, if the surface potential is high, the variation of mobility as a function of Ka has a maximum; if it is low, the mobility increases monotonically with Ka. Here, the mobility is mainly determined by the drag force, rather than by the electric force, acting on the particle as in the case where the particle is positively charged and the cavity uncharged. If both the particle and the cavity are charged, the electrophoretic behavior of the particle can be deduced from the results of the above two cases.