One of the predominant cell-cycle programs found in mature tissues is endoreplication, also known as endoreduplication, that leads to cellular polyploidy. A key question for the understanding of endoreplication cycles is how oscillating levels of cyclin-dependent kinase activity are generated that control repeated rounds of DNA replication. The APC/C performs a pivotal function in the mitotic cell cycle by promoting anaphase and paving the road for a new round of DNA replication. However, using marker lines and plants in which APC/C components are knocked down, we show here that outgrowing and endoreplicating Arabidopsis leaf hairs display no or very little APC/C activity. Instead we find that RBX1-containing Cullin-RING E3 ubiquitin-Ligases (CRLs) are of central importance for the progression through endoreplication cycles; in particular, we have identified CULLIN4 as a major regulator of endoreplication in Arabidopsis trichomes. We have incorporated our findings into a bio-mathematical simulation presenting a robust two-step model of endoreplication control with one type of cyclin-dependent kinase inhibitor function for entry and a CRL-dependent oscillation of cyclin-dependent kinase activity via degradation of a second type of CDK inhibitor during endoreplication cycles.