Structurally altered or marker chromosomes are the cytogenetic hallmarks of cancer cells, but their origins are still debated. Here we propose that aneuploidy, which is ubiquitous in cancer and inevitably unbalances thousands of synergistic genes, destabilizes the structure of chromosomes by catalyzing DNA breaks. Aneuploidy catalyzes such breaks by unbalancing teams of enzymes, which synthesize and maintain DNA and nucleotide pools, and even unbalancing histones via the corresponding genes. DNA breaks then initiate deletions, amplifications, and intra- and interchromosomal rearrangements. Our hypothesis predicts that the rate at which chromosomes are altered is proportional to the degree of aneuploidy: the more abnormal the number and balance of chromosomes, the higher the rate of structural alterations. To test this prediction, we have determined the rates at which clonal cultures of diploid and aneuploid Chinese hamster cells generate new, and thus nonclonal, structurally altered chromosomes per mitosis. Based on about 20 metaphases, the number of new, structurally altered chromosomes was 0 per diploid, 0-0.23 per near-diploid, 0.2-1.4 per hypotriploid, 3.25-4.8 per hypertriploid, and 0.4 per near-tetraploid cell. Thus, instability of chromosome structure increases exponentially with the deviation of ploidy from the normal diploid and tetraploid balances. The particular chromosomes engaged in aneuploidy also affected the rates of chromosome alteration, particularly at low aneuploidy indices. We conclude that aneuploidy is sufficient to cause structural instability of chromosomes. Further, we suggest that certain structurally altered chromosomes encode cancer-specific phenotypes that cannot be generated by unbalancing intact chromosomes. We also extend the evidence for aneuploidy causing numerical instability of chromosomes autocatalytically, and adduce evidence that aneuploidy can cause the many gene mutations of cancer cells that have been attributed to various mutator genes.