The rate of spontaneous generation and the frequency of carcinogen-induced anchorage-independent variants of preneoplastic rat tracheal epithelial (RTE) cells in culture were quantitated. Anchorage-independent variants of different RTE cell lines arose spontaneously by a stochastic process at rates of 0.5 X 10(-4) to 5.4 X 10(-4) variants/cell/generation, as determined by fluctuation analyses. These variants were also induced by the mutagen N-methyl-N'-nitro-N-nitrosoguanidine with a frequency of approximately 10(-3) variants/surviving cell. The rates of spontaneous change and the frequencies of induction are the first reported for epithelial cells and are similar to some, although not all, rates and frequencies of change to anchorage independence for fibroblast-like cells in culture. In addition, these rates and frequencies are similar to those for mutations at some known gene loci. The induced frequency of this late change in neoplastic progression is, however, considerably lower than the frequency of induction of the initial, preneoplastic changes in RTE cells in culture (approximately 3 X 10(-2)/surviving cell). These quantitative determinations are useful in defining the mechanisms of late changes occurring during the progression of RTE cells to the neoplastic state.