Transformation of cells in culture by chemical carcinogens or X rays seems to require at least two steps. The initial step is a frequent event; for example, after transient exposure to either methylcholanthrene or X rays, almost every cell of established lines of mouse embryo fibroblasts proved capable of yielding transformed, tumorigenic descendants. Although results were interpreted as indicating that 100% of the progeny of methylcholanthrene-treated cells were potentially transformed, later experiments showed that only a very small minority of the progeny of cells initiated by X rays or methylcholanthrene actually produced transformed colonies. We thus concluded that there must be a second step in transformation that is a very rare event. We assumed that this event occurred after the cultures became confluent, a time when transformed cells have a selective growth advantage. Since then, however, others have shown that transformation can occur soon after initiation and that clones of transformed cells may already be present by the time initiated cultures become confluent. It has been hypothesized that the second step behaves like a spontaneous mutation in having a constant but small probability of occurring each time an initiated cell divides. We show here that the clone size distribution of transformed cells in growing cultures initiated by X rays is, indeed, exactly what would be expected on that hypothesis.