An apparatus and method for identifying containers (1) containing different anesthetic fluids. A connecting element (8) is used for coupling the container with a conduit (6) extending to a patient for supplying an anesthetic to a patient. The containers containing anesthetic fluids are designated or labeled distinctly from each other by means of at least one magnetic-field producing element (12). The presence of this element is in turn detected by means of a magnetic-field detecting element (13). The identification of a container containing an anesthetic fluid and, thus, an anesthetic fluid contained therein is effected by means of an identification element (15), which receives a signal from one or more magnetic-field detecting elements. The detection can also be used as a basis for establishing whether the container is coupled in its position.