Two species of stick insect with a distinctive morphology, Candovia evoneobertii (Zompro & Adis, 2001) and Echetlus fulgens Zompro, 2004, were considered to be native to Australia and introduced into Brazil. However, Heteronemia dubia (Caudell, 1904) and Heteronemia fragilis (Brunner von Wattenwyl, 1907), both described more than a hundred years ago from South America, exhibit striking similarities with the two purportedly introduced species and are found to be conspecific with C. evoneobertii. Careful analysis of the literature and specimens revealed that these species belong to the Neotropical tribe Diapheromerini (Diapheromeridae) and represent a new genus, Arumatia Ghirotto gen. nov. We therefore propose Arumatia fulgens (Zompro, 2004) gen. et comb. nov. and Arumatia dubia (Caudell, 1904) gen. et comb. nov. We further redescribe A. dubia (Caudell, 1904) gen. et comb. nov. based on several specimens and synonymize Heteronemia fragilis syn. nov. and Candovia evoneobertii syn. nov. under it. Additionally, five new Brazilian species are described: Arumatia diamante Ghirotto gen. et sp. nov. from Abaíra, Bahia; Arumatia aramatia Ghirotto gen. et sp. nov. from Porto Nacional, Tocantins; Arumatia motenata Ghirotto gen. et sp. nov. from Serra do Cipó, Minas Gerais; Arumatia crassicercata Ghirotto, Crispino & Engelking gen. et sp. nov. from Alto Paraíso de Goiás, Goiás; and Arumatia anyami Ghirotto, Crispino & Neves gen. et sp. nov. from Costa Marques, Rondônia. Species of Arumatia gen. nov. occur mostly in the Cerrado domain, and represent the first Diapheromeridae recorded in this area. Most species are known exclusively from females with only A. aramatia gen. et sp. nov. and A. motenata gen. et sp. nov. known from both sexes. Adult and egg morphology are described and illustrated in detail for all species, as well as the nymph stages for A. dubia. Biological observations are presented, including parthenogeny in A. dubia and one of the few detailed accounts of sexual behaviour in Euphasmatodea (for A. motenata gen. et sp. nov.). Finally, a species of Diapheromerini described in error from Brazil, Diapheromera armata Piza, 1973, is synonymized under the North American Megaphasma denticrus (Stål, 1875) (syn. nov.).