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.