The self-diffusion of the polymer and oil (i.e., tert-butylbenzene) components in aqueous ternary cubic liquid crystalline (clc) mesophases formed by three different Pluronic triblock copolymers (i.e., P94, F68, and F127) has been investigated using pulsed-field gradient (PFG) NMR. For the polymer chains, the diffusion has been compared to that determined in corresponding aqueous binary (without oil) de mesophases and micellar solution phases. The polymer chain diffusion is Fickian (i.e., Gaussian) in the micellar solution state and becomes anomalous in the clc mesophases. A pronounced departure from a single-exponential spin-echo attenuation of the polymer chains in the de mesophases is observed. The self-diffusion of the oil component in the ternary de mesophases is Fickian. Compared to the self-diffusion of the pure oil at the same temperature, it is found that the diffusion is reduced by a factor of 10(3) in the de mesophases. This clearly demonstrates that the de mesophases consist of closed aggregates with the oil solubilized in the micelles. A possible scenario for the observed polymer chain and the oil diffusion behavior is discussed, based partly on PFG NMR results obtained from a binary aqueous de sample of the surfactant dodecyl trimethylammonium chloride (DOTAC).