Abstract: The system has a reader of electronic labels comprising several devices for the transmission/reception of electromagnetic waves, offset angularly about a median axis so that, when the reader is placed in the vicinity of a label and irrespectively of their relative orientation, at least a part of the lines of the magnetic field generated by at least one of said transmission/reception devices can get looped by passing into the coil of the label in the direction of its axis. The label has a foil made of amagnetic and conductive material placed against the antenna and parallel to it to form a reflective screen for the electromagnetic waves. Application to the contact-free identification of objects, notably metal objects, such as gas cylinders.