Despite the complexity and variety of biological oscillators, their core design invariably includes an essential negative feedback loop. In the Xenopus laevis embryonic cell cycle oscillator, this loop consists of the kinase cyclin B–Cdk1 and the ubiquitin ligase APC/C^Cdc20; active Cdk1 activates APC/C^Cdc20, which then brings about cyclin B degradation and inactivates Cdk1. Here we ask how this negative feedback loop functions quantitatively, with the aim of understanding what mechanisms keep the Cdk1–APC/C^Cdc20 system from settling into a stable steady state with intermediate levels of Cdk1 and APC/C^Cdc20 activity. We found that the system operates as a time-delayed, digital switch, with a time lag of ∼ 15 min between Cdk1 and APC/C^Cdc20 activation and a tremendously high degree of ultrasensitivity (n_H≈17). Computational modelling shows how these attributes contribute to the generation of robust, clock-like oscillations. Principles uncovered here may also apply to other activator–repressor oscillators and help in designing robust synthetic clocks.