The sedimentation of a nonconducting spherical particle in a spherical cavity is analyzed theoretically. We show that, for the case where the former is positively charged and the latter uncharged, the sedimentation velocity of the particle decreases with kappa a, kappa and a being respectively the reciprocal Debye length and the radius of a particle. If the surface potential of the particle phi(r) is high, the sedimentation potential has a local maximum as kappa a varies, which becomes inappreciable if the surface potential is low. If phi(r) is sufficiently high, the sedimentation potential has a local maximum as lambda (= radius of particle/radius of cavity) varies. It is not observed, however, if kappa a is large. If an uncharged particle is placed ina positively charged cavity, the sedimentation potential may reverse its sign, and may have a local minimum as kappa a varies.