A method of detecting and localizing a source of partial discharge in an electrical apparatus placed in an enclosure containing an acoustically-conductive fluid. The method consists in: positioning (31) acoustic detectors and acquiring the positions of the detectors; defining (35) groups of detectors, each group including at least three detectors; ensuring (37) that each group is free from any triangle having vertices embodied by three detectors in which at least one angle lies outside a range of angles, and otherwise eliminating the group; for each non-eliminated group, calculating (38) an approximate position for the source; ensuring (39) that each non-eliminated group is free from any triangle having vertices embodied by two detectors of the group and by the approximate position, including at least one angle that lies outside the range, and otherwise eliminating the group; and calculating (43) the looked-for position of the source by averaging the approximate positions of all or some of the non-eliminated groups.