We examine the hypothesis that global scale episodes of anoxia such as occurred in the Cretaceous are due to high productivity and/or stagnation of the circulation. Two modes of ocean circulation are considered: a thermohaline overturning cell, essentially vertical, which involves global scale upwelling into the surface followed by sinking in deep water formation regions; and an approximately horizontal cell which connects the abyss directly with deeply convecting waters in deep water formation regions. Modern analogs for these processes are formation of North Atlantic Deep Water and Antarctic Bottom Water, respectively. Over most of the oceans the surface new production is nutrient limited and thus directly proportional to the supply of nutrients by the vertical overturning cell. A reduction in oxygen can only be brought about by increased vertical overturning associated with increased production. In addition, the model shows that as the deep ocean becomes lower in oxygen, the sensitivity of the oxygen levels to the meridional circulation decreases such that it becomes difficult or impossible to achieve complete anoxia. This relative insensitivity of deep ocean oxygen levels to the magnitude of the vertical overturning cell and associated surface production may explain why it has been difficult to establish a clear connection between high surface productivities in low and mid-latitudes and anoxia. In deep water formation regions, on the other hand, new production is not nutrient limited. A reduction in abyssal oxygen can be brought about by high productivity in such regions and/or by stagnation of the horizontal circulation cell, in accordance with the stagnation hypothesis. Furthermore, the sensitivity of the deep ocean oxygen to the processes occurring in deep water formation regions increases as oxygen levels decrease. We therefore suggest that processes occurring in deep water formation regions may be the critical ones in determining deep ocean oxygen.