Hypoxys is one of four subgenera of Edessa (Fabricius, 1787) together with Aceratodes (De Geer, 1773), Dorypleura (Lepeletier & Serville, 1825) and Edessa (Fabricius, 1787). This taxon has a very confusing taxonomy due to incorrect use of the names available, imprecise descriptions, and large number of very similar species. To illustrate the confusion, Hypoxys potentially includes a large number of species of Edessa, but actually contains only the type species, according to the most recent catalogue. The name E. quadridens Fabricius, 1803, type species of Hypoxys, was used for more than a century as a label to identify a large group of similar species. In this work we continue revising Edessa elevating Hypoxys to genus based on the following morphological characters: proximal part of costal margin black; evaporatorium with a deep notch on lateral margin; anterior arms of metasternal process acuminate; pygophore longer than wide and subrectangular or barrel-shaped in dorsal view; dorsal rim of pygophore well-projected, almost reaching posterolateral angles and finishing in a small lobe; and posterolateral angles of pygophore not developed. Hypoxys is being divided in four species groups to include 17 species transferred from Edessa. H. quadridens group comprises: Hypoxys quadridens (Fabricius, 1803) (type species), H. boerneri (Breddin, 1904) comb. nov., H. claricolor (Breddin, 1907) comb. nov., H. dolosus (Breddin, 1907) comb. nov., H. eburatulus (Breddin, 1907) comb. nov., H. necopinatus (Breddin, 1907) comb. nov., H. offuscatus (Breddin, 1907) comb. nov. and H. trabeculus (Breddin, 1907) comb. nov. H. triangularis group comprises: H. triangularis (Dallas, 1851) comb. nov. (type species), H. capito (Breddin, 1904) comb. nov. and H. subrastratus (Bergroth, 1891) comb. nov. H. oxyacanthus group comprises: H. oxyacanthus (Breddin, 1904) comb. nov. (type species), H. brachyacanthus (Breddin, 1904) comb. nov., H. infulatus (Breddin, 1904) comb. nov., H. leptacanthus (Breddin, 1904) comb. nov. and H. tragelaphus (Breddin, 1903) comb. nov. H. balteatus group comprises only H. balteatus (Walker, 1868) comb. nov. These groups of species will be useful to organize the new species of Hypoxys that will be described in upcoming papers. Descriptions, measurements, photos of genitalia of both sexes; photos in dorsal and ventral views of the species; and distribution maps are provided. Males of H. capito, H. claricolor, H. eburatulus, H. infulatus, and H. subrastratus are described for the first time. Female of H. necopinatus is described for the first time. Edessa jugalis is considered a junior synonym of H. quadridens; E. rimata a junior synonym of H. offuscatus; E. scabriventris and E. leprosula junior synonyms of H. triangularis; E. pachyacantha a junior synonym of H. tragelaphus; E. orba a junior synonym of E. oxyacanthus. A key to the species of Hypoxys is also provided.