Rhythms in the pseudo-steady state (PSS) levels of reactive species (RS), particularly superoxide and hydroxyl radicals, exist in cancer cells. The RS rhythm characteristics, particularly frequency and amplitude, are entrained (reset) by the anticancer compounds/drugs. In this work, we show for the first time that the phase of the RS rhythm at which the drug is added is significantly important in determining the cytotoxicity of anticancer compounds/drugs such as menadione and curcumin, in two different cancer cell lines. Curcumin, the more effective of the two drugs (IC50 = 15 µM, SiHa; 6 µM, HCT116) induced reset of superoxide and hydroxyl rhythms from 15.4 h to 9 h, and 25 h to 11 h respectively, as well as caused increases in these radical levels. However, menadione (IC50 = 20 µM, SiHa; 17 µM, HCT116) affected only the superoxide levels. Drug treatment at different time points/phase of the RS rhythm resulted in a maximum of 27% increase in cytotoxicity, which is significant. Further, we report for the first time, an unexpected absence of a correlation between the intracellular PSS RS and antioxidant levels; thus, the practice of using antioxidant enzyme levels as surrogate markers of intracellular oxidative stress levels may need a re-consideration. Therefore, the RS rhythm could be a fundamental/generic target to manipulate for improved cancer therapy. © 2020, The Author(s).