Although a single transition in the cell cycle is both sufficient and necessary to account for the distribution of differences in the intermitotic times of sister cells, two random transitions seem necessary to account for the responses of quiescent cells to stimulation by growth factors. We propose that serum-depleted quiescent cells "rest" in an indeterminate state (Q) which they leave at random upon stimulation and initiate a lengthy process (L). Upon completion of L the cells enter another indeterminate state (A) which they also leave at random and shortly thereafter initiate S phase and subsequently divide. On leaving A they also re-enter Q, and, again at random, initiate L. This sequence, Q leads to L leads to A, is maintained in steady state proliferation, and because of the random exit from Q and A, overlaps to varying degrees with the conventional cell cycle (M-G1-S-G2-M). The hypothesis provides a qualitative account of various problematic features of the lag between stimulation and entry into S phase. It also provides a good quantitative account of the distribution of sibling differences, the correlation coefficient of sibling intermitotic times and the distribution of intermitotic times and the distribution of intermitotic times in steady state growing cultures. There are striking similarities between the hypothetical cycle and the centriole cycle.