The study of the Paschen-Back effect in hyperfine structure is of particular interest as it is the only possibility to verify the complete theory of the gradual change of the Zeeman effect from weak to strong fields, as there are no suitable multiplets available for this purpose. The theory of the Zeeman effect for any field strength has been studied by Heisenberg and Jordan [Zeits. f. Physik. 37, 263 (1926)] and by Darwin [Proc. Roy. Soc. A115, 1 (1927)] for the case of ordinary multiplets. There may be shown to be a very close analogy between ordinary multiplets and the hyperfine structure separations, the former being due to the interaction between the total extranuclear moment and the nuclear moment