The Cape Floristic Region ('fynbos biome') has very high levels of plant species diversity and endemism. Much of this diversity is concentrated in a relatively small number of clades centered in the region (Cape clades), and these form a vegetation called 'fynbos'. The general explanation for the origin of this diversity is that much of it evolved in the Pliocene and Late Miocene in response to progressive aridification. We present a phylogenetic analysis of an almost complete species sample of the largest clade of Restionaceae, the third largest Cape clade. This indicates that the radiation of the Restionaceae started between 20 and 42 Myr ago, and since then there were no, or at most gradual, changes in the speciation rate in this clade. For seven other clades, the estimated starting dates for their radiation ranges from 7 to 20 Myr ago. Combining the radiation patterns for these clades shows that ca. 15% of the modern species evolved during the Pleistocene, and almost 40% since the beginning of the Pliocene. We suggest that these clades might have radiated in response to the fynbos vegetation increasing its extent in the Cape as a result of climatic change.