Mutant clonogenic cells, resistant to individual chemotherapeutic agents, are known to play a central role in clinical chemotherapy failure. The possibility that mutant cells, resistant to conventionally fractionated megavoltage photon radiotherapy, exist in human tumors is considered. Applying the mutation theory of Luria and Delbruck to describe the appearance of resistant cells, several conclusions follow: (a) the mean number of resistant cells in a tumor will be determined by the tumor size and the mutation rate; (b) a wide variation in radiosensitivity in tumors of the same histology is expected, because of a large variation in the number of resistant cells that they contain; (c) the presence of a resistant clone will not reduce the tumor-control probability until the tumor becomes sufficiently large; (d) initial response will not be a reliable predictor of long-term control; (e) clonogenic assays may not accurately predict treatment outcomes; (f) the mutation rate may be the most accurate predictor of tumor aggressiveness and resistance to various treatment modalities; (g) tumors with a low mutation rate, which may include seminoma, Hodgkin's disease and many pediatric tumors would be curable by either chemotherapy or radiation; (h) pleomorphic tumors with a high mutation rate, which may include glioblastoma multiforme, would be difficult to cure by any means. Clinical and experimental evidence is reviewed for the existence of radioresistant cell lines in human and animal tumors, and further experiments are proposed to test this hypothesis. Treatment strategies for targeting radioresistant clones are discussed.