A mathematical model is proposed for the relationship between the bacterial cell processes resulting in the initiation of DNA replication that are responsible for DNA and protein synthesis. It is assumed that one or several precursors of DNA synthesis act as a trigger for the replication system of both the bacterial and episomal DNA present. By mathematical analysis it is shown that this model yields a stable cell cycle with a regulated cell volume at the time of intiation of DNA replication. Some proposals resulting from the model are experimentally proved with E. coli strains lysogenic for the γ bacteriophage, the DNA of which is an example of episomal DNA. The initiation timing of phage DNA replication is in accordance with the model, in that the mode and duration of inhibition of bacterial DNA replication causes the accumulation of DNA precursors leading to the initiation of replication of bacterial and episomal DNA.