Transverse nuclear spin relaxation measurements, employing the Carr-Purcell-Meiboom-Gill (CPMG) sequence, represent a powerful tool to stud), the dynamics of director fluctuations in liquid crystalline mesophases. Generally, however, the analysis of these experiments requires a slow-motional theory based on the stochastic Liouville equation. In this paper, such an approach is applied to stud), the shape fluctuations of dimyristoyl-phosphatidylcholine membrane vesicles with controlled size. Analysis of the transverse nuclear spin relaxation rates, measured as a function of the pulse frequency in the CPMG sequence, provides values for the bending rigidity, kappa, and the lateral tension, sigma, of the membrane vesicles. The results are of major importance in the understanding of the biological membrane function.