Mitosis is controlled by the specific and timely degradation of key regulatory proteins, notably the mitotic cyclins that bind and activate the cyclin-dependent kinases (Cdks). In animal cells, cyclin A is always degraded before cyclin B, but the exact timing and the mechanism underlying this are not known. Here we use live cell imaging to show that cyclin A begins to be degraded just after nuclear envelope breakdown. This degradation requires the 26S proteasome, but is not affected by the spindle checkpoint. Neither deletion of its destruction box nor disrupting Cdk binding prevents cyclin A proteolysis, but Cdk binding is necessary for degradation at the correct time. We also show that increasing the levels of cyclin A delays chromosome alignment and sister chromatid segregation. This delay depends on the proteolysis of cyclin A and is not caused by a lag in the bipolar attachment of chromosomes to the mitotic spindle, nor is it mediated via the spindle checkpoint. Thus, proteolysis that is not under the control of the spindle checkpoint is required for chromosome alignment and anaphase.