SUMMARY.Although some of the details of the structure of Lyomeri have been rather carefully studied, as for instance the minute structure of the gut, kidneys, of some bones and cartilages by Nussbaum‐Hilarowiez, and the proportions of parts of the body by Bertin, the main characters of Lyomeri have not attracted the attention of scientists and the systematic position of the group is most uncertain.The Lyomeri have a branchial apparatus built differently from other fiches; the Lyomeri have no proper gill cover and no bones supporting such cover. InEury‐pharynxthere aresixfunctional visceral clefts andfiveholobranchs (inSaccopharynxthe hind cleft and the hind gill are reduced). The bone forming the upper jaw of Lyomeri lies medially to the hyomandibular, mandibular and the quadrate. The radials of the lobate pectorals articulate with the basal cartilages of the lobes but not with the pectoral girdle. The rays of the fins of Lyomeri are ossified, but soft and not segmented. The disposition of the series of the lateral line on the head is unusual. There is a series along the edge of the upper jaw, a series along the suspensorium, and one parallel to the suspensorium along the cheek, from the orbit to the posterior end of the opercular fold. There is no lateral line along the mandible.Several more characters of Lyomeri stress the peculiarity of this group. The Lyomeri have no supraoccipital, and no lateral ethmoids; the prootics ofEurypharynxextend anteriorly into the interorbital septum beyond the hypophysis and the trigeminus‐facialis ganglion; parts of the neurocranium are movably articulated; the cover bones of the roof of the cranium are unusual; there are no vomer arid parasphenoid inSaccopharynx(these bones are present, but much reduced inEurypharynx).It seems possible, from the present study, that the upper jaw of Lyomeri is formed by the elements of the mandibular arch, that the anterior visceral cleft of Lyomeri is not a branchial but a prehyoid cleft, and that the cartilages supporting the septum behind this cleft are the ‘missing’ ventral elements of the hyoid arch*.However, as in the specimens studied by me the cephalic nerves are partly lost their course could not be followed.Thus these two main features of Lyomeri still remain uncertain.An attempt at a general characterization of Lyomeri and of the two fanlilich of this group is made in Part II of this paper. In Part III a brief comparison of Lyomeri with the Osteichthyes generally, and with some peculiar Actinopterygians, is given.In Part I the specimens of Lyomeri of the British Museum are described in sonic detail, their systematic position is discussed, and a brief revision of the species ofSaccopharynxandEurypharynxis given.This work was done in rather an uncomfortable time and conditions. It was much delayed by the absence of books, and of many fishes preserved in the British Museum which had been evacuated for safety, and by the lack of various other facilities.All the drawings and diagrams were made by the writer.The system of fishes used here for the main groups is that adopted by Forster‐Cooper (1940), and for the orders that used by Regan (1929).The names of parts of the skeleton used here are mainly as used by de Beer (1937); references to the terminology of Holmgren and Stensio (1936) are also given.I am most grateful to the Zoological Society of London and to the Linnean Society for permission to use their libraries. I am much indebted to Dr. E. Trewavas of the British Museum for most helpful discussions and advice, and for kindly reading part of the manuscript. I tender my most sincere thanks to Prof. G. R. de Beer, F.R.R., for kindly discussing with me this paper and for his criticisms and