Several studies point to the existence of a disturbance in the metabolism of the reactive species of oxygen in cancer cells. Based on this evidence, and in particular on a characteristic behaviour of tumour membrane lipids, namely their growth-related resistance to oxy-radical-induced peroxidation, a sequence of events is outlined that could hypothetically drive the transformed cell to an uncontrolled proliferation. The proposed scheme is also conceived as a framework for further in vivo investigations of the complex biological phenomena of tumour cell growth and invasion in more integrated and kinetically controlled cellular systems.