In this paper we present a new approach to the analysis of electrochemical impedance spectroscopy (EIS) data for electrodes covered by passivating surface films that grow in time. The impedance of such electrodes increases in time due to the gradual growth of their thickness as well as to the change of their local characteristics. The growing part of the surface films may either be homogeneous in its structure and properties or inhomogeneous, with gradually changing properties as a function of the distance of the newly formed surface species from the metal-film interface. We show herein that the time-difference impedance spectra (DIS), i.e., the difference between two complex impedance curves, Z(omega, t(1)) - Z(omega, t(2)), measured after different periods of storage, tl and t(2), as a function of frequency may provide a very useful tool for characterizing the nature of the growing passivating films. These time-difference impedance curves (e.g., plotted in coordinates Z(imag) vs Z(real)) can be simulated both for homogeneous growing surface films on electrodes and for situations in which local properties such as the surface film's resistivity are nonuniform across the growing film. The prospects of this approach have been demonstrated in the analysis of the surface films at lithium electrodes freshly prepared and stored in alkyl carbonate mixture (ethylene-dimethyl carbonates) with a Li salt, and measured periodically by EIS. The analysis of DIS of this system has shown that during a period of several hours after the electrode's preparation in solution, the process of the surface film deposition is very complicated. Properties of the new portions of the film are varying in time so that the deposited film possesses a highly nonuniform structure. Moreover, the local characteristics of earlier formed portions are modified gradually inside the film. However, as the storage time is longer, the growth of the surface Films on the lithium electrodes becomes more homogeneous, probably due to the increased selectivity of the Li-solution reactions when the surface films are thicker.