Local coupling between nitrogen fixation and denitrification in current biogeochemical models could result in runaway feedback in open-ocean oxygen minimum zones (OMZs), eventually stripping OMZ waters of all fixed nitrogen. This feedback does not seem to operate at full strength in the ocean, as nitrate does not generally become depleted in open-ocean OMZs. To explore in detail the possible mechanisms that prevent nitrogen depletion in the OMZ of the eastern tropical South Pacific (ETSP), we develop a box model with fully prognostic cycles of carbon, nutrients and oxygen in the upwelling region and its adjacent open ocean. Ocean circulation is calibrated with Δ<sup>14</sup>C data of the ETSP. The sensitivity of the simulated nitrogen cycle to nutrient and oxygen exchange and ventilation from outside the model domain and to remineralization scales inside an OMZ is analysed. For the entire range of model configurations explored, we find that the fixed-N inventory can be stabilized at non-zero levels in the ETSP OMZ only if the remineralization rate via denitrification is slower than that via aerobic respiration. In our optimum model configuration, lateral oxygen supply into the model domain is required at rates sufficient to oxidize at least about one fifth of the export production in the model domain to prevent anoxia in the deep ocean. Under these conditions, our model is in line with the view of phosphate as the ultimate limiting nutrient for phytoplankton, and implies that for the current notion of nitrogen fixation being favoured in N-deficit waters, the water column of the ETSP could even be a small net source of nitrate.