The trajectory of at least one marine animal emitting sound signals in the form of series of clicks, such as a cetacean, is passively determined. During successive processing time windows, raw analog signals are acquired from a plurality of hydrophones disposed in a marine environment and converted into digital data. Digital data filtering eliminates spurious noises and keeps the data, for each pair of hydrophones and each processing window, that corresponds to potential values (TDOAs) for the time-difference of arrival of the sound signals at two different hydrophones. For each hydrophone pair, the consistency of the TDOAs is checked and a number of filtered and mutually-consistent TDOAs are selected. Based on the filtered and mutually-consistent TDOAs, the successive instantaneous positions of the click sources are determined by means of nonlinear regression, and the trajectory of at least one marine animal in the environment is deduced in real time.