The monotypic genus Odontonuncia Hickman, 1958 is redescribed. A new closely related genus, Hickmanoxyomma, is described for the type species, H. cavaticum (Hickman,1958), and six other species. Two new combinations are established: H. cavaticum (Monoxyomma) and H. tasmanicum (Roewer,1915) (Monacanthobunus). One new synonymy is proposed: Monoxyomma silvaticum Hickman, 1958 =H. tasmanicum (Roewer, 1915). Five new species are described in three species groups: H. goedei, H. clarkei and H. eberhardi (cavaticum species group); H. gibbergunyar (tasmanicum species group); and H. cristatum (cristatum species group). The distribution of the six cavernicolous and one surface species in Hickmanoxyomma and the possible influence of Pleistocene glaciation are discussed. Cavernicolous adaptations, including reductions in lateral branches of claws, are described. Free lateral sclerites are recorded for the first time in the Triaenonychidae and their significance as a family character in the superfamily Travunioidea is discussed.