RESUMEN
Hypoxys was recently raised from a subgenus of Edessa to a genus. In the same work Hypoxys was divided in four groups of species: H. quadridens; H. triangularis; H. oxyacanthus and H. balteatus, gathering 17 species transferred from Edessa. The H. balteatus group was recently revised and 15 species were added to this originally monotypic group. Several new species await description in other groups. The H. quadridens group is composed by very similar species; therefore, their main diagnostic features are found in the male genitalia. In this work we describe 17 new species belonging to H. quadridens group: H. angulatus sp. n., H. bitumidus sp. n., H. clavatum sp. n., H. crassimarginatum sp. n., H. cristatus sp. n., H. dorsocarinatus sp. n., H. excavatus sp. n., H. flexuosus sp. n., H. nigrosinuatus sp. n., H. omegoides sp. n., H. pentagonalis sp. n., H. rugulosus sp. n., H. runcinatus sp. n., H. similis sp. n., H. trilobulatus sp. n., H. unguiculatus sp. n., H. ventrotuberculatus sp. n.. Diagnosis, photographs of the external genitalia, body in dorsal and ventral view, and distribution map are provided, including a key to the species of the group.