The circadian clock coordinates an organism's growth, development and physiology with environmental factors. One illuminating example is the rhythmic growth of hypocotyls and cotyledons in Arabidopsis thaliana. Such daily oscillations in leaf position are often referred to as sleep movements or nyctinasty. Here, we report that plantlets of the liverwort Marchantia polymorpha show analogous rhythmic movements of thallus lobes, and that the circadian clock controls this rhythm, with auxin a likely output pathway affecting these movements. The mechanisms of this circadian clock are partly conserved as compared to angiosperms, with homologs to the core clock genes PRR, RVE and TOC1 forming a core transcriptional feedback loop also in M. polymorpha.