When cells from mass cultures of chick embryo fibroblasts are grown at very low density, some cells yield large clones while others produce smaller clones, and some cells fail to divide at all. The distribution of clone sizes is related to the number of population doublings which the donor mass culture has undergone: the more doublings which have occurred, the smaller the average clone size. In this report we describe a model which analyses this phenomenon, referred to as 'clonal attenuation', in detail. The model is based on the concept that a cell with hypothetically unlimited replicative potential--i.e. a 'stem' cell--can become 'committed' to a programme of limited replicative potential. This event is assumed to be stochastic and to have a fixed probability per stem cell division. The parameters of the model are: Pc, the probability of commitment; N, the number of differentiative divisions; and Tc, the cell-cycle times. By computer simulation, it is shown that Pc increases roughly exponentially at each successive stem cell division. According to the model, when the daughter of a stem cell becomes committed, its progeny proceed through N obligatory divisions before becoming terminally differentiated (post-mitotic). The best-fit value of N was found to be seven. The simulations also reveal that the absolute number of stem cells in the total population increases for most of the lifespan of the culture. When Pc becomes much greater than 0.5, the number of stem cells declines rapidly to zero, and the culture nears senescence. Sensitivity analysis shows that Pc can assume only a limited range of values at each stem-cell division.