In deuterium (H-2) NMR spectroscopy of fluid lipid bilayers, the average structure is manifested in the segmental order parameters (S-CD) of the flexible molecules. The corresponding spin-lattice relaxation rates (R-1Z) depend on both the amplitudes and the rates of the segmental fluctuations, and indicate the types of lipid motions. By combining H-2 NMR order parameter measurements with relaxation studies, we have obtained a more comprehensive picture of lipids in the liquid-crystalline (L-alpha) state than formerly possible. Our data suggest that a lipid bilayer constitutes an ordered fluid, in which the phospholipids are grafted to the aqueous interface via their polar headgroups, whereas the fatty acyl chains are in effect liquid hydrocarbon. Studies of H-2-labeled saturated lipids indicate their R-1Z rates and S-CD order parameters are correlated by a model-free, square-law functional dependence, signifying the presence of relatively slow bilayer fluctuations. A new composite membrane deformation model explains simultaneously the frequency (magnetic field) dependence and the angular anisotropy of the relaxation. The results imply the R-1Z rates are due to a broad spectrum of 3-D collective bilayer excitations, together with effective axial rotations of the lipids. For the first time, NMR relaxation studies show that the viscoelastic properties of membrane lipids at megahertz frequencies are modulated by the lipid acyl length (bilayer thickness), polar headgroups (bilayer interfacial area), inclusion of a nonionic detergent (C12E8), and the presence of cholesterol, leading to a range of bilayer softness. Our findings imply the concept of elastic deformation is relevant on lengths approaching the bilayer thickness and less (the mesoscopic scale), and suggest that application of combined R-1Z and S-CD studies of phospholipids can be used as a simple membrane elastometer. Heuristic estimates of the bilayer bending rigidity kappa and the area elastic modulus K-a enable comparison to other biophysical studies, involving macroscopic deformation of thin membrane lipid films. Finally, the bilayer softness may be correlated with the lipid diversity of biomembranes, for example, with regard to membrane curvature, repulsive interactions between bilayers, and lipid-protein interactions.