The geologic record preserves evidence that vast regions of ancient oceans were once anoxic, with oxygen levels too low to sustain animal life. Because anoxic conditions have been postulated to foster deposition of petroleum source rocks and have been implicated as a kill mechanism in extinction events, the genesis of such anoxia has been an area of intense study. Most previous models of ocean oxygen cycling proposed, however, have either been qualitative or used closed-system approaches. We reexamine the question of anoxia in open-system box models in order to test the applicability of closed-system results over long timescales and find that open and closed-system modeling results may differ significantly on both short and long timescales. We also compare a scenario with basinwide diffuse upwelling (a three-box model) to a model with upwelling concentrated in the Southern Ocean (a four-box model). While a three-box modeling approach shows that only changes in high-latitude convective mixing rate and character of deepwater sources are likely to cause anoxia, four-box model experiments indicate that slowing of thermohaline circulation, a reduction in wind-driven upwelling, and changes in high-latitude export production may also cause dysoxia or anoxia in part of the deep ocean on long timescales. These results suggest that box models must capture the open-system and vertically stratified nature of the ocean to allow meaningful interpretations of long-lived episodes of anoxia. ¿ 2000 American Geophysical Union