Analysis of the nuclear spin relaxation rates of lipid membranes provides a powerful means of studying the dynamics of these important biological representatives of soft matter. Here, temperature-and frequency-dependent H-2 and C-13 nuclear magnetic resonance (NMR) relaxation rates for vesicles and multilamellar dispersions of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) in the liquid-crystalline slate have been fitted simultaneously to various dynamic models for different positions of the acyl chains. The data include H-2 R-1Z rates (Zeeman order of electric quadrupolar interaction) acquired at 12 external magnetic field strengths from 0.382 to 14.6 T, corresponding to a frequency range from omega(D)/2 pi=2.50-95.3 NMz; and 2H R-1Q rates (quadrupolar order of electric quadrupolar interaction) at 15.3, 46.1, and 76.8 MHz. Moreover, C-13 R-1Z data (Zeeman order of magnetic dipolar interaction) for DMPC are included at six magnetic field strengths, ranging from 1.40 ro 17.6 T, thereby enabling extension of the frequency range to effectively (omega(C)+omega(H))/2 pi=938.7 MHz. Use of the generalized approach allows formulation of noncollective segmental and molecular diffusion models, as well as collective director fluctuation models, which were tested by fitting the H-2 R-1Z data at different frequencies and temperatures (30 degrees C and 50 degrees C). The corresponding C-13 relaxation rates were predicted theoretically and compared to experiment, thus allowing one to unify the C-13 and H-2 NMR data for bilayer lipids in the fluid state. A further new aspect is that the spectral densities of motion have been explicitly calculated from the H-2 R-1Z and R-1Q data at 40 degrees C. We conclude that the relaxation in fluid membrane bilayers is governed predominantly by relatively slow motions. which modulate the residual coupling remaining from faster local motions (order fluctuations). Only the molecular diffusion model, including an additional slow motional process, and the membrane deformation model describing three-dimensional collective fluctuations fit the H-2 NMR data and predict the C-13 NMR data in the MHz range. Orientational correlation functions have been calculated, which emphasizes the importance of NMR relaxation as a unique tool for investigating the dynamics of Lipid bilayers and biological membranes. (C) 1997 American Institute of Physics. [S0021-9606(97)01447-5].