We apply new statistical methods to a recent estimate of the phylogeny of all living primate species to test a range of models of cladogenesis. Null models in which probabilities of speciation and extinction do not differ among contemporaneous lineages are not consistent with the phylogeny. We present evidence that the net rate of cladogenesis (speciation rate minus extinction rate) increased in the lineage leading to the Cercopithecidae (Old World monkeys), and that there have been further increases in some lineages within that family. Such increases suggest the occurrence of clade selection, although we have not identified the selected trait or traits. There is no evidence that the net rate of cladogenesis is a function either of how many primate lineages are already present or of time. Intriguingly, three other major clades-Strepsirhini, Platyrrhini and Hominoidea-appear to have had very similar rates of clade growth, in spite of their great biological differences.