Tropical forests contain the majority of extant plant diversity and their role as a cradle and/or museum of biodiversity is an important issue in our attempts to assess the long-term consequences of global climate change for terrestrial biomes. Highly diverse groups of liverworts are an often ignored but extremely common element in rainforests, and thus their evolution may shed light on the ecological robustness of rainforest biomes to climate fluctuations. We record a remarkable constant accumulation of diversity through time for the most species-rich family of liverworts, Lejeuneaceae, inferred by divergence time estimates. The observed pattern supports the recently developed concept of a dual role of the tropics as both a museum and a cradle of biodiversity.