The arctic amphipoda collected by the Willem Barents’ expeditions of 1878 and 1879 were described by Dr. P. P. C. Hoek. The same eminent carcinologist had already carried out the preliminary sorting of the present collection, when, upon appointment to his important post at Helder, he found that the time requisite for describing it was no longer at his command. Under these circumstances at his suggestion Professor Max Weber did me the honour of asking for my services, and the following paper is the result. Of the sixty species here recorded the majority are already well known. They include a very large number of the most striking forms among the Gammaridea. The specific names in the list are due to a score of authors, concerning whom, as writers on Amphipoda, it may be said that they have among them not only most of the best but also the best out of most. For fifteen of the species mentioned science is indebted to the elaborate accuracy of Kröyer, whose high qualities appear to be a kind of heirloom in the Scandinavian school of naturalists. That the Amphipoda should have been in the first instance best studied by northern observers is, however, not surprising. For, compared with the forms of these Crustacea commonly met with in Dutch and English waters, the Arctic species claim attention and respect by gigantic size, a bristling armature, brilliant colouring, or prodigious swarms. They cannot be overlooked and ignored, as their kindred practically are in England. In regard to many of the established species and genera I have not given a full synonymy, but have thought it sufficient to refer to the Bibliography annexed to my Report on the Challenger Amphipoda. In view of the full descriptions published elsewhere, and especially in the admirable work on the Crustacea of Norway by G. O. Sars, now in course of publication, I have usually limited myself to an occasional comment or identifying note upon existing genera or species. In a few instances detailed descriptions of old species have been given, in each case, as will be easily perceived, to serve a special purpose. Five new species are described. Though this may seem an inconsiderable number in so fine a collection, nevertheless, when it is remembered who have been the reapers of the harvest of Arctic amphipoda during the last fifty years, this late gleaning will not fall short of any reasonable expectations. To judge by the results obtained at Kerguelen Island in the Southern Ocean, it is much rather in Antarctic than in Arctic waters that the explorer who devotes himself to the search after Amphipoda may hope to find new and surprising forms. There are, it is true, some remarkable instances in which the same species occurs both far north and far south, but these are after all not very numerous.