We present experimental measurements and analysis of the dynamics and the phase behaviour of saturated DMPC and unsaturated DOPC oriented multi-lamellar bilayers. Elastic and inelastic neutron scattering were used to directly probe the dynamical processes of these membrane systems on time and length scales relevant to the internal and localized motion of lipid monomers. Mobility in this regime can be informative in elucidating the local interactions responsible for material properties of these fluid lipid systems. DMPC and DOPC are structurally similar in terms of their membrane hydrophobic thickness; however, they exhibit different mechanical properties in terms of both elastic compressibility and bending moduli. The analyses suggest that the constraint imposed by the double bonds in DOPC acyl chains restricts atomic motion in both liquid and gel phases compared to DMPC. We discuss applications of molecular dynamics to further elucidate the atomic details of the dynamical processes. Such an understanding may suggest how membrane properties can be tuned using a variety of different lipid species.