Structural and dynamical properties of membrane domains are crucial for understanding the function of these domains in eukaryotic cells. Due to the difficulty of examining and interpreting the intricacies of membrane organization in live cells, model membranes composed of ternary mixtures of saturated and unsaturated lipids and cholesterol are considered a sufficient model for studies of biomembranes. Over many years, large (>1 micron) liquid-ordered domains that form in such model membranes (e.g. DOPC/SM/Chol) have been studied and closely linked to lipid rafts in cells. Lipid rafts exist in vivo as domains of much smaller sizes on the order of 100 nm. Observing domains on a smaller length-scale (i.e. closer to the size of lipid rafts in vivo) has proven to be a non-trivial task due to limitations of spatial resolution of many techniques suitable for such studies. Recently, nanosized domains have been observed in model membranes. This work presents studies of lipid self-diffusion in such membranes (DOPC/SM/Chol and DOPC/DPPC/Chol) using PFG NMR with high gradient strengths. Application of high gradients affords diffusion studies for sufficiently small diffusion times under the conditions of the narrow gradient pulse approximation. The latter is essential for recording artifact-free diffusion data. As a result, observing diffusion behavior in lipid membranes on length scales comparable with the sizes of lipid rafts in vivo becomes possible. The results of these studies show the dependence (or independence) of diffusion behavior of lipids on diffusion time due to the exchange of lipid molecules between the lipid-ordered and the surrounding liquid-disordered domains at temperatures sufficiently below the transition temperature. Using PFG NMR with high gradient strengths, it now becomes possible to directly study and compare lateral diffusion of lipids inside large (>1 micron) and nanosized (~100 nm) domains as well as to investigate lateral transport of lipids through the domain boundaries.