The illaenid collection, which comprises about 550 specimens housed in the Paleontologisk Museum, Oslo, was almost entirely obtained by Kiær during his investigations of the Silurian stratigraphy of the Oslo district. T owards the end of his classical memoir Kiær gave short descriptions, but without illustrations, of five new species of lllaenus and six new species and one variety of Bumastus, all of which had pro ved useful as indices of age (1908, pp. 571 578). His intention was to produce an amply illustrated monograph, and several photographs and drawings were made, a num ber of specimens were expertly prepared from technically difficult rock, and nearly one third of the collection was provisionally identified. Before the monograph was completed, Kiær's interest was diverted to Devonian vertebrates and to the fossiliferous Cambrian rocks of Tømten, and he never returned to finish his research. Owing to a certain amount of confusion regarding those of Kiær's Ja beis on which specific names alone were written, I have not been able to trace all his new species, while there are others which in my opinion are insufficiently preserved to warrant description. Thus of his list, lllaenus rotundus, l. sculptus, l. longispinosus, l. postremus, Bumastus depressus, B. longicaudatus, and B. injlatus are described, but l. brøggeri, B. brevis, B. perbrevis, and B. sulcatus, var. convexus have not been recognized; B. praeruptus of Kiær, is considered to be synonymous with B. bouchardi and one new species, l. norvegicus, and one new variety, B. sulcatus, var. kiaeri, are added to the list. Furthermore, in his short diagnoses, Kiær described pygidia and cranidia under the same name when there is no real evidence that they belong to the same species. Several excellently preserved cephala, cranidia and pygidia are present in the collection but the majority of the material is fragmentary. The pygidia of l. rotundus, l. sculptus, and B. sulcatus, var. kiaeri are definitely known, but in all cases where there is no indication that a pygidium actually belongs to a certain cranidium, I have preferred to allocate no name to the pygidium but to describe it as Type A and so on to Type F. Such a procedure dispenses with the possibility of confusion likely to arise by mixing pygidia and cranidia of different species. There are a few more species represented in the collection than are described in this paper, but the material is either too poorly preserved or I have hesitated to erect new terms when, as in some cases, a single specimen is available. My thanks are due to Dr. Anatol Heintz and Dr. Leif Størmer for providing the opportunity for studying the collection, to Mr. F. W. Anderson, Dr.]. Koliha, Dr. Stensii:i, and Mr. T. H. Withers for the loan of specimens, to Mr. E. W. Seavill for assistance with the photographic work, and to the Colston Research Society of the University of Bristol.