The invention provides a leak-monitoring system for space-enclosing objects and coupling regions lying therebetween, as well as an associated method. The invention relates to a leak-monitoring system (2) for space-enclosing objects such as pipes (4), hoses or containers that have a surrounding wall (6), and comprising at least one electrically-conductive element that acts as a leak sensor (8) and is mounted on or integrated into said surrounding wall (6). According to the invention, in order to allow simple and reliable monitoring of imminent or existing leaks even for large wall areas, and as universally as possible for different types of medium, said electrically-conductive element is a component of a measurement bridge (12) that comprises an evaluation device for (20) for the bridge voltage (VMess) and that is supplied, by a voltage source (18), with an operating voltage (UG) having both alternating voltage components and direct voltage components.