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- Abrocoma – chinchilla rats
- Aplodontidae – mountain beavers
- Bathyergidae – mole-rats
- Capromyidae – hutias
- Castoridae – beavers
- Caviidae – cavies
- Chinchillidae – chinchillas, viscachas
- Ctenodactylidae – gundis, Speke’s pectinators
- Ctenomyidae – tuco-tucos
- Dasyproctidae – acouchis, agoutis, pacas
- Dinomyidae – pacaranas
- Dipodidae – jerboas
- Echimyidae – coro-coros, spiny rats
- Erithizontidae – coendous, porcupines
- Geomyidae – pocket gophers, taltuzas
- Glidiridae – dormice
- Heptaxodontidae – (n/a)
- Heteromyidae – kangaroo rats, pocket mice
- Hydrochaeris – capybaras
- Hystricidae – porcupines
- Muridae – gerbils, hamsters, lemmings, mice, rats, voles
- Octodontidae – deguses, rats
- Pedetidae – springhares
- Petromyidae – dassie rats
- Sciuridae – chipmunks, marmots, prairie dogs, squirrels
- Seleviniidae – desert dormice
- Thryonomyidae – cane rats
- Zapodidae – birch mice, jumping mice
