The fully natatory families of the janiroidean Asellota, the unnopsids sensu lato, include a group of genera that blurs the distinction between the Ilyarachnidae and the Eurycopidae. This work determines the interrelationships of the ilyarachnid-like eurycopids, and shows that they are a monophyletic group. In so doing, the family-level systematics of the munnopsids is revised. The ilyarachnid-like eurycopids are assigned to a newly constituted subfamily, the Lipomerinae, and five genera are described, four of which are new. A diagnosis of the subfamily Lipomerinae with a key to the superspecific taxa is included in the taxonomic part. One species in each superspecific taxon is fully described. Coperonus n. gen. is a primarily Southern Hemisphere group with several species in the south Atlantic and around the Antarctic continent. The most ilyarachnid-like genus is Hapsidohedra n. gen., which may have a cosmopolitan distribution. Lionectes n. gen. is found in Antarctic waters. The pan-Atlantic genus Lipomera Tattersall is further divided into three new subgenera. One of these subgenera, L. (Tetracope) n. subgen., has a coiled gut, a rare occurrence among Crustacea. The cosmopolitan Mimocopelates n. gen. is represented by a North Atlantic species group based on the species M. longipes n. sp., and an equatorial species M. anchibraziliensis n. sp. Character analyses of most munnopsid genera present the characters that reveal relationships between taxa. The character states were assigned evolutionary polarities by comparison with characters in a presumed munnopsid sister group, the Acanthaspidiidae, and other janiroidean families. Computerized phylogenetic analyses produced cladograms that were not fully resolved, but had significantly lower homoplasy values than a tree based on previous classifications. The Lipomerinae were the most significantly monophyletic group of the munnopsid taxa, and a consensus tree of all possible cladograms confirmed the monophyly of the Lipomerinae. Because the previous classifications of the families were not consistent with the most parsimonious cladograms, the following proposals are made: all munnopsid families should be placed into one large family, the Munnopsidae; the Ilyarachnidae and the Munnopsidae sensu stricto should be demoted to subfamilial status; and the current subfamilies of the Eurycopidae should be retained. This new classification recognizes the monophyly of the Lipomerinae within the Munnopsidae. Alternatives to this classification are discussed. Supporting the text are appendices illustrating and defining morphological terms.