SummaryIn order to transmit a eukaryotic cell’s genome accurately from mother cell to daughter cells, it is essential that the basic events of the cell division cycle (DNA synthesis and mitosis) occur once and only once per cycle, i.e., that a cell progresses irreversibly from G1 to S to G2 to M and back to G1. Irreversible progression through the cell cycle is assured by a sequence of ‘latching’ molecular switches, based on molecular interactions among cyclin-dependent kinases and their auxiliary partners. Positive feedback loops (++ or −−) create bistable switches with latching properties, and negative feedback loops drive progression from one stage to the next. In budding yeast (Saccharomyces cerevisiae) these events are coordinated by double-negative feedback loops between Clb-dependent kinases (Clb1-6) and their antagonists (APC:Cdh1 and Sic1). If the coordinating signal is compromised, either by deletion of Clb1-5 proteins or expression of non-degradable Clb2, then irreversibility is lost and yeast cells exhibit multiple rounds of DNA replication or mitotic exit events (Cdc14 endocycles). Using mathematical modelling of a stripped-down control network, we show how endocycles arise because the switches fail to latch, and the gates swing back and forth by the action of the negative feedback loops.