Analysis of discharge curves in time-domain IP experiments is the key step from data acquisition to interpretation, and hence requires major effort to improve accuracy and reliability. Under the assumption that discharge curves may be represented by a superposition of real exponentials, we present in this paper a method of analysis based on Prony’s theorem. Its main advantages are the possibility of automatic determination of the number of exponential terms and of evidencing complex exponentials. The relation to the Cole-Cole method is also discussed, and a tentative procedure is suggested for the evaluation of the Cole-Cole spectral parameters by Prony’s algorithm. Finally, an example of laboratory experiments on samples of Neapolitan yellow tuff is given to demonstrate the applicability of the new method.