In this essay we have considered possible relationships between errors in DNA replication and malignant progression. Theoretical and experimental studies designed to determine the energy of interaction between different nucleotides have been reviewed. The difference of the energy of interaction between complementary and noncomplementary base pairs (1 to 3 kcal) is not sufficient to account for the exactness of DNA replication that is observed in vivo or in vitro. Thus, DNA polymerases must play a role in base selection. This point has been established by the detection of polymerases that copy polynucleotide templates with few errors and the detection of others that make many errors. Different mechanisms for base selection by polymerases have been considered. Our findings that both extracts of human leukemic lymphocytes and a purified DNA polymerase from avian myeloblastosis virus have exceptionally high error rates have been considered in relationship to oncogenesis. A hypothesis is presented that relates mistakes in DNA replication, as promoted by error-prone DNA polymerases, to tumor progression. We have also considered a more general concept encompassing early cellular changes that lead to oncogenesis. The justification for this essay is that both of these hypotheses are open to immediate experimental analysis.