The accumulation of oncogenic alleles of cancer genes (proto-oncogenes and tumor suppressor genes) within the body's cells is the major process underlying carcinogenesis. These alleles can originate from somatic mutagenesis during mitosis of stem cells (acquired alleles), while others are passed on from one generation to another through the germline (inherited alleles). The persistence of inherited oncogenic alleles in populations is not fully understood from an evolutionary point of view. Indeed, these alleles increase the probability of developing a cancer, and thus decrease the survival and fertility of their carriers. They should therefore be purged over evolutionary times. Using theoretical approaches, we test hypotheses based on the reduction of the fitness effects of these deleterious alleles, which would allow their maintenance within populations.