The dynamics of nanosized colloidal particles dispersed in a hyper-swollen lyotropic lamellar phase of a nonionic surfactant has been studied by ac electrophoretic light scattering and direct tracking of particles under a microscope. The frequency spectrum of electrophoretic mobility shows two relaxation processes. These are originated from the hindrance of free diffusion of particles by the interaction between membranes and particles. By direct tracking measurement, we find that particles jump from site to site where they stay for a long time. This trap-jump process greatly decreases the mobility at low frequencies.