Randomly proliferating 3Y1stD123 cells are arrested in G1 phase within 24 h after a shift up to 39.8°C (temperature arrest), yet the density-arrested cells (prepared at 33.8°C) enter S phase at 39.8°C with serum stimulation, with or without preexposure to 39.8°C for 24 h (Zaitsu and Kimura 1984a). When the density-arrested 3Y1tsD123 cells were preexposed to 39.8°C for 96 h, they lost the ability to enter S phase at 39.8°C by serum stimulation and required a longer lag time to enter S phase at 33.8°C by serum stimulation than did the cells not preexposed to 39.8°C. Simian virus 40 induced cellular DNA synthesis at 39.8°C in the density-arrested 3Y1tsD123 preexposed to 39.8°C for 96 h. In the absence of serum after a shift down to 33.8°C, the temperature-arrested 3Y1stD123 cells entered S phase and then divided once. We postulate from these results that (1) that ts defect in 3Y1tsD123 is involved in a serum-independent process. Once this process is accomplished, its accomplishment is invalidated slowly with preexposure to 39.8°C. This and the serum-dependent processes occur in parallel but not necessarily simultaneously. The accomplishment of both (all) processes is required for the initiation of S phase. The density-arrested 3Y1tsD123 cells have accomplished the serum-independent process related to the ts defect, but have not accomplished serum-dependent processes. In case of the temperature-arrested 3Y1tsD123 cells, the reverse holds true. The lag time for entry into S phase depends on the preparedness for the initiation of DNA synthesis (on the extent of accomplishment of each of all processes required for entry into S phase). (2) To induce cellular DNA synthesis, simian virus 40 stimulates directly the serum-independent process. However, we do not rule out the possibility that simian virus 40 stimulates serum-dependent processes simultaneously.