Two-dimensional electron-electron double resonance (2D-ELDOR) is a technique that is sensitive to the dynamical processes affecting spin labels in complex fluid environments. In ordered fluids, such as membrane vesicles, the 2D-ELDOR experiment is affected by the molecular tumbling in the locally ordered environment. This motion occurs on two different time scales, the faster molecular motion relative to the local director, and the slower collective fluctuations of the director field. In the experimental study of Patyal, Crepeau, and Freed (Biophys. J. 1997, 73, 2201), it was found that the widths of the autopeaks of the 2D-ELDOR spectrum increased as a function of the mixing time. In the present work, a theory is developed for the effects of director fluctuations on the autopeaks in the 2D-ELDOR experiment by employing an analytical solution of the stochastic Liouville equation for which the director field is treated as a multidimensional Gaussian process, as previously developed by Frezzato, Kothe, and Moro (J. Phys. Chem. B 2001, 105, 1281 and J. Phys. Chem. B 2004, 108, 9505). Good agreement is found between theory and experiment, notably the only adjustable parameter is k, the bending elastic modulus of the membrane. The values of k = 11 x 10(-20) J for 1,2-dipalmitoyl-sn-glycero-phosphatidylcholine (DPPC) vesicles and k = 15 x 10(-20) J for DPPC/gramicidin A (5:1) vesicles, both at 45 degrees C, were found from the analysis and agree well with previous related measurements by other physical techniques. This establishes 2D-ELDOR as a useful technique to study the elastic properties of biological membranes.