Three inkless octopodids are described from the continental shelf off southeastern South America. These octopuses are a non-commercial by-catch in the Falkland Islands fishery. Muusoctopus eureka (Robson, 1929) is one of two common inkless octopuses and is of medium size, with orange-pink skin and a distinctive pattern of irregular dark markings, interspersed with white spots visible only in living or freshly dead specimens. The second common inkless octopus is M. longibrachus akambei, a new subspecies of the Chilean species Muusoctopus longibrachus (Ibáñez, Sepúlveda and Chong, 2006). It has slender arms and is much larger at full maturity than M. eureka. It is a plain orange color when alive, pinkish cream when preserved. Muusoctopus bizikovi, sp. nov., is a smaller, rarer species, colored wine-red whether alive or preserved, and has a vestigial ink duct between the digestive gland and the anus. Relations with other species are discussed. This group of octopuses has often been associated with the genus Benthoctopus Grimpe, 1921, which is a junior synonym of Bathypolypus Grimpe (a genus of small species characterized by much shorter arms and males with a robust copulatory organ bearing transverse lamellae). It is argued that the misleading characterization of the so-called Benthoctopus group of species as “smooth skinned” is based upon the artefactual appearance of specimens fixed and preserved suboptimally following a detrimental freeze-thaw cycle of fisheries material previously frozen while at sea.