Models of ocean circulation and biogeochemical cycles are used to speculate about possible mechanisms of deep-sea anoxia across the Permo-Triassic boundary. Two modes of likely Late Permian ocean thermohaline circulation are identified: a vigorous "thermal mode" driven by cooling in southern polar latitudes and a weaker "haline mode" driven by evaporation from the subtropics. We find that the thermal mode, typical of climates such as our own, is unlikely to surpport deep-sea anoxia. The haline mode, which might exist in warm climates with enhanced hydrological cycles, can lead to significant but periodic depletion of oxygen in the Panthalassic deep ocean. However, owing to the inherent instability of the haline mode, a deep-sea anoxia persisting for millions of years is not clearly supported by this study, though mechanisms emerge which might be consistent with the observed record. The enhanced hydrological cycle (or reduced oceanic diapycnal mixing) required to obtain the haline mode remain unconstrained for the Late Permian.