Incoherent quasi-elastic neutron scattering is applied to study the local diffusion and chain dynamics of L-alpha-diplamiotylphosphatidylcholine molecules in oriented model membranes. Different motions are distinguished by changing the hydration of the multilayers as well as by measuring below and above the gel-to-liquid crystalline phase transition. The time range of the utilized time-of-flight spectrometer permits to observe two types of motion to be observed more closely: chain defect motions and the local diffusion of the whole molecule in its solvation cage. Oriented lipid membranes are a useful system for the observation of chain defects, as they can be macroscopically oriented, in contrast to most polymers. As a representative model for a chain defect a kink is chosen and the corresponding scattering functions are derived. The kink motion can explain the entire dynamics seen in the gel phase, and the lifetime of such a defect was found to be 10-15 ps, in good agreement with theoretical predictions. On the other hand the dynamics in the liquid crystalline phase cannot be explained even by a superposition of several kinks and thus requires the consideration of an additional motion: the local diffusion of the molecule in its solvation cage. The size of the solvation cage is increasing with multilayer hydration and reduced temperature. Particularly interesting in view of recent discussions about the origin of the short-range repulsive forces between membranes is the experimental finding of an out-of-plane motion with an amplitude of 1-1.5 A, which cannot be explained by the undulation of the whole membrane.