Oscillations in cyclin-dependent kinase (CDK) activity drive the somatic cell cycle. After entry into mitosis, CDKs activate the anaphase-promoting complex (APC), which then promotes cyclin degradation and mitotic exit. The re-accumulation of cyclin A causes the inactivation of APC and entry into S phase, but how cyclin A can accumulate in the presence of active APC has remained unclear. Here we show that, during G1, APC autonomously switches to a state permissive for cyclin A accumulation. Crucial to this transition is the APC(Cdh1)-dependent autoubiquitination and proteasomal degradation of the ubiquitin-conjugating enzyme (E2) UbcH10. Because APC substrates inhibit the autoubiquitination of UbcH10, but not its E2 function, APC activity is maintained as long as G1 substrates are present. Thus, through UbcH10 degradation and cyclin A stabilization, APC autonomously downregulates its activity. This indicates that the core of the metazoan cell cycle could be described as a self-perpetuating but highly regulated oscillator composed of alternating CDK and APC activities.