Inherent or acquired drug resistance is a major obstacle for the successful treatment of cancers. Many mechanisms of drug resistance have been described including a decreased drug uptake, an increase in DNA damage repair, enhanced drug detoxification, an altered level or mutation of the intracellular drug target or an increased drug efflux from the cell. Most of these mechanisms impinge upon the interaction of a drug with its cellular target or immediate consequences of such as interaction. For example, a decrease in the cellular levels of topoisomerase II thwarts the efficacy of certain topoisomerase II inhibitors, and enhanced levels of glutathione increase resistance to DNA alkylating agents. However, some tumours are inherently resistant to all chemotherapeutic agents, i.e. with different mechanisms of action. What is the mechanism(s) underlying this pleiotropic drug resistance? One possibility is that such drug-resistant tumour cells have an abnormally high threshold for the engagement of apoptosis (programmed cell death). The suppression of apoptosis as a mechanism for drug resistance is discussed in this article.