The effects of the anesthetic dibucaine on the relaxation kinetics of the gel-liquid crystalline transition of dipalmitoylphosphatidylcholine (DC16PC) multilamellar vesicles have been investigated using volume-perturbation calorimetry. The temperature and pressure responses to a periodic volume perturbation were measured in real time. Data collected in the time domain were subsequently converted into and analyzed in the frequency domain using Fourier series representations of the perturbation and response functions. The Laplace transform of the classical Kolmogorov-Avrami kinetic relation was employed to describe the relaxation dynamics in the frequency domain. The relaxation time of anesthetic-lipid mixtures, as a function of the fractional degree of melting, appears to be qualitatively similar to that of pure lipid systems, with a pronounced maximum, tau max, observed at a temperature corresponding to greater than 75% melting. The tau max decreases by a factor of approximately 2 as the nominal anesthetic/lipid mole ratio increases from 0 to 0.013 and exhibits no further change as the nominal anesthetic/lipid mole ratio is increased. However, the fractional dimensionality of the relaxation process decreases monotonically from slightly less than two to approximately one as the anesthetic/lipid mole ratio increases from 0 to 0.027. At higher ratios, the dimensionality appears to be less than one. These results are interpreted in terms of the classical kinetic theory and related to those obtained from Monte Carlo simulations. Specifically, low concentrations of dibucaine appear to reduce the average cluster size and cause the fluctuating lipid clusters to become more ramified. At the highest concentration of dibucaine, where n < 1, the system must be kinetically heterogeneous.