One of the most important antioxidant enzymes is superoxide dismutase (SOD), which catalyzes the dismutation of superoxide radicals to peroxide. The gene for CuZnSOD lies in humans on chromosome 21, and its activity is increased in patients with Down syndrome. However, instead of being beneficial, increased lipid peroxidation is associated with this increased expression, and also studies on bacteria and transgenic animals show that high levels of SOD actually lead to increased lipid peroxidation and hypersensitivity to oxidative stress. Using mathematical models, we investigated the question of how overexpression of SOD can lead to increased oxidative stress, although it is an antioxidant enzyme. We considered several possibilities that have been proposed in the literature, such as CuZnSOD-catalyzed hydroxyl radical formation, superoxide-mediated inhibition of membrane peroxidation, and short-circuiting of the Cu(I)ZnSOD/Cu(II)ZnSOD redox cycle. We found that one of the proposed mechanisms under certain circumstances is able to explain the increased oxidative stress caused by SOD. Furthermore, we identified an additional mechanism that agrees well with experimental observations. We call it the "alternative pathway" mechanism, because it depends on superoxide radicals having alternative pathways besides their reaction with SOD. The alternative pathway mechanism is a very general explanation for SOD-associated oxidative stress, because it does not depend on the specific type of SOD, nor on the redox status of the cell. We therefore think that it might be the common mechanism for the detrimental effects seen in cells and organisms with increased levels of the different forms of superoxide dismutase.