The electrophoretic behavior of a nonrigid entity, e.g., liquid entity or bubble, in a spherical cavity is analyzed theoretically taking the effect of double-layer polarization into account. We show that the electrophoretic mobility of the entity decreases as the ratio (viscosity of surrounding fluid/viscosity of medium inside entity) decreases and its surface potential decreases. If the surface potential is sufficiently high, double layer polarization has the effect of producing a local minimum in the electrophoretic mobility as double layer thickness varies. If the double layer is thick, depending upon the level of surface potential, the limiting electrophoretic mobility when the viscosity ratio is much larger than unity (e.g., gas bubble in liquid) is about 5-10 times of that when the viscosity ratio is much smaller than unity (e.g., rigid particle in liquid). For a thin or medium-thick double layer, the limiting electrophoretic mobility when the viscosity ratio is much larger than unity is about 3 times of that when the viscosity ratio is much smaller than unity. The presence of cavity wall has the effect of retarding the electrophoretic mobility.