Family: Anomaluridae (scaly-tailed squirrels)
Family: Aplodontiidae (mountain beaver)
Family: Castoridae (beavers)
Family: Heteromyidae (kangaroo rats, kangaroo mice)
Family: Diatomyidae (Laotian rock rat)
Family: Ctenodactylidae (gundis)
Family: Bathyergidae (African mole rats)
Family: Hystricidae (old world porcupines)
Family: Abrocomidae (chinchilla rats)
Family: Capromyidae (hutias)
Family: Ctenomyidae (tuco-tucos)
Family:
Dasyproctidae (agoutis)
Azara's Agouti (Dasyprocta azarae)
Coiban Agouti (Dasyprocta coibae)
Crested Agouti (Dasyprocta cristata)
Black Agouti (Dasyprocta fuliginosa)
Orinoco Agouti (Dasyprocta guamara)
Kalinowski Agouti (Dasyprocta kalinowskii)
Brazilian Agouti (Dasyprocta leporina)
Mexican Agouti (Dasyprocta mexicana)
Black-rumped Agouti (Dasyprocta prymnolopha)
Central American Agouti (Dasyprocta punctata)
Ruatan Island Agouti (Dasyprocta ruatanica)
Green Acouchi (Myoprocta pratti)
Red Acouchi (Myoprocta acouchy)
Family: Dinomyidae (pacaranas)
Family: Echimyidae (spiny rats)
Family: Myocastoridae (nutria)
Family: Octodontidae (octodonts)
Family: Dipodidae (jerboas, jumping mice)
Family: Calomyscidae (mouse-like hamsters)
Family: Cricetidae (hamsters, new world rats, mice, voles)
Family: Gliridae (dormice)
Family: Muridae (true mice, rats, gerbils, spiny mice, crested rat)
Family: Nesomyidae (climbing mice, rock mice, white-tailed rat, Malagasy rats, mice)
Family: Pedetidae (springhares)
Family: Petromuridae (dassie rat)
Family: Platacanthomyidae (spiny dormice)
Family: Spalacidae (mole rats, bamboo rats, zokors)
Family: Thryonomyidae (cane rats)
