Organelles called centrosomes in metazoans or spindle pole bodies (SPBs) in yeast direct the assembly of a bipolar spindle that is essential for faithful segregation of chromosomes during mitosis. Abnormal accumulation of multiple centrosomes leads to genome instability, and has been observed in both tumour cells and cells with targeted mutations in tumour-suppressor genes. The defects that lead to centrosome amplification are not understood. We have recapitulated the multiple-centrosome phenotype in budding yeast by disrupting the activity of specific cyclin-dependent kinase (CDK) complexes. Our observations are reminiscent of mechanisms that govern DNA replication, and show that specific cyclin/CDK activities function both to promote SPB duplication and to prevent SPB reduplication.