A device for detecting lightning strikes (9) on an electrically insulating structure (11) likely to be subjected to a lightning strike, for example an aircraft radome, includes on an external surface (12) one or more lightning arrester strips (10), made of an electrically conductive material and electrically linked to an electrically conductive structure. At least one inductive sensor (3) is positioned near the internal surface (13) of the electrically insulating structure so that the inductive sensor delivers a signal when a lightning arrester strip is passed through by a lightning current I. The signals from the inductive sensor, for example a flat coil or two flat coils mounted in opposition, are received and processed by acquisition means.