The G2-M checkpoint in the cell cycle is identified with a set of phosphorylation-dephosphorylation (PD) cycles involving Cdc25 and the maturation-promoting factor (MPF); these PD cycles are coupled in a way that generates an instability. This instability arises out of a transcritical bifurcation which could be exploited by the G2 DNA damage checkpoint pathway in order to arrest or delay entry into mitosis. The coupling between PD cycles involving Wee1 and MPF does not lead to an instability and therefore Wee1 may not be a crucial target of the checkpoint pathway. A set of PD cycles exhibiting transcritical bifurcation also possesses the integrative ability of a checkpoint for 'checking' that prerequisites are satisfied prior to the next cell cycle event. Such a set of coupled PD cycles is suggested to be a core mechanism of cell cycle checkpoints.