Background/aim: In this study, we evaluated Thymus revolutus Célak essential oil and its two main constituents, γ-terpinene and p-cymene, as potential oxidative agents against lung cancer and epidermoid carcinoma cells. Materials and methods: Cell viability assessment was made by CellTiter-Blue® cell viability and 3-(4,5-dimethylthiazol-2-yl)-2,5- diphenyltetrazolium bromide (MTT) assay after treatment with 5?600 ?g/mL concentrations of essential oil, γ-terpinene, and p-cymene. Malondialdehyde and 8-hydroxy-2'-deoxyguanosine levels in parental H1299, epirubicin-resistant (drug-resistant) H1299, A549, and A431 cells were also assayed after essential oil, γ-terpinene, and p-cymene had been administered for 24 h. Glutathione S-transferase (GST), glutathione peroxidase (GPx), glutathione reductase (GRx), and glucose 6-phosphate dehydrogenase (G6PD) activities were determined. Results: Parental H1299 cells were found to be more sensitive to the cytotoxic effects of all compounds. While A431 cells had the highest membrane damage, which was caused by essential oil (IC50 and IC70), A549 cells had the highest DNA damage at IC50 and IC70 p-cymene concentrations. G6PD, GST, GRx, and GPx enzyme activities of cells, which increased against these compounds, depended on concentrations, incubation times, and antioxidant capacities of the cells. Conclusion: This study suggests that different cancer cells showed different cellular responses against potential antitumor and prooxidative effects of the essential oil and its two main constituents.