Between 100 kHz and 2 GHz ultrasonic attenuation spectra of two aqueous solutions of vesicles from 1,2-dimyristoyl-L-3-phosphatidylcholine have been measured at 13 temperatures around the main phase transition temperature of the membranes. The spectra are analyzed in terms of an asymptotic high frequency background contribution and three relaxation terms. Two of these terms can be represented by a discrete relaxation time, respectively, the other one extends over a significantly broader frequency range than a Debye-type relaxation term. It was found to nicely follow the predictions of the Bhattacharjee-Ferrell model of three-dimensional critical fluctuations. This finding has been additionally verified by measurements of the scaling function and by an analysis of the relaxation rate of order parameter fluctuations following from the fit of the experimental scaling function data to the theoretical form. Theoretical arguments are presented to indicate why the three-dimensional theory applies so well to the quasi-two-dimensional membrane system. (C) 2003 American Institute of Physics.