Cete was named by Linnaeus (1758). It is extant.

It was reranked as the family Cete by Illiger (1811); it was reranked as the suborder Cete by Gray (1863), Gray (1864) and Gray (1866); it was reranked as the unranked clade Cete by McKenna (1975); it was misspelled as Cetae by Gray (1825), Gray (1850), Bonaparte (1850), Gill (1871), Hay (1930), Archibald (1998) and Hulbert and Whitmore (2006).

It was assigned to Natantia by Illiger (1811); to Pinnata by Bonaparte (1850); to Cetacea by Gray (1863), Gray (1864) and Gray (1866); to Educabilia by Gill (1871); to Monodelphia by Hay (1930); to Ungulata by McKenna (1975); to Cetungulata by Archibald (1998); and to Mammalia by Linnaeus (1758), Gray (1825), Gray (1850) and Hulbert and Whitmore (2006).