We use an automaton model for the cell cycle to assess the toxicity of various circadian patterns of anticancer drug delivery so as to enhance the efficiency of cancer chronotherapy. Based on the sequential transitions between the successive phases G1, S (DNA replication), G2, and M (mitosis) of the cell cycle, the model allows us to simulate the distribution of cell cycle phases as well as entrainment by the circadian clock. We use the model to evaluate circadian patterns of administration of two anticancer drugs, 5-fluorouracil (5-FU) and oxaliplatin (l-OHP). We first consider the case of 5-FU, which exerts its cytotoxic effects on cells in S phase. We compare various circadian patterns of drug administration differing by the time of maximum drug delivery. The model explains why minimum cytotoxicity is obtained when the time of peak delivery is close to 4a.m., which temporal pattern of drug administration is used clinically for 5-FU. We also determine how cytotoxicity is affected by the variability in duration of cell cycle phases and by cell cycle length in the presence or absence of entrainment by the circadian clock. The results indicate that the same temporal pattern of drug administration can have minimum cytotoxicity toward one cell population, e.g. of normal cells, and at the same time can display high cytotoxicity toward a second cell population, e.g. of tumour cells. Thus the model allows us to uncover factors that may contribute to improve simultaneously chronotolerance and chronoefficacy of anticancer drugs. We next consider the case of oxaliplatin, which, in contrast to 5-FU, kills cells in different phases of the cell cycle. We incorporate into the model the pharmacokinetics of plasma thiols and intracellular glutathione, which interfere with the action of the drug by forming with it inactive complexes. The model shows how circadian changes in l-OHP cytotoxicity may arise from circadian variations in the levels of plasma thiols and glutathione. Corroborating experimental and clinical results, the simulations of the model account for the observation that the temporal profiles minimizing l-OHP cytotoxicity are in antiphase with those minimizing cytotoxicity for 5-FU.