Abstract: A system containing a writing and reading unit with an antenna coil and at least one preferably elastic carrier in the form of a strip, on which is provided at least one mobile data memory which has a memory and operating circuit and, connected thereto, an elongate loop coil. The arrangement has the advantage that the mobile data memory can be provided on surfaces having virtually any degree of undulation. If a mobile data memory of this type encloses the circumference of a cylindrical object, then data transmission can be carried out in any desired radial spatial direction. The device is particularly suitable for identifying gas cylinders, in which case the elastic carrier, in the form of a strip, of a mobile data memory is placed around the casing of each gas cylinder, particularly in the region of the neck rings thereof.