An ocean model has been developed which, for prescribed physics, deals with interrelationships between chemical distributions, biogeochemical sinks and sources, chemical reactions at redox fronts, and transports across the air‐sea and sediment‐water interfaces. In its first application here, the model focuses on biogeochemical cycling of phosphorus, nitrogen, oxygen, and sulphur in an ocean forced by river input of nutrients. This is a natural starting point for a global climate model since ocean circulation and biology determine atmospheric CO2 concentrations for a given inventory of inorganic C and oceanic production is controlled mainly by the availability of inorganic P and/or N. A general approach is taken to look at oxic versus anoxic conditions, P versus N limitation of primary production, with or without inorganic removal of phosphate to the sediments. As demanded by this approach, the model is nonlinear and continuous in a vertical coordinate. To focus on the biogeochemical aspects, ocean physics are kept as simple as possible. Cold, oxygen‐rich water sinks at high latitudes and is upwelled with a constant velocity. Turbulent mixing is parameterized with a constant, vertical diffusion coefficient. The biogeochemical processes considered are new production, burial, nitrogen fixation, phosphorite formation, and three types of organic decomposition: oxidation with O2, denitrification, and sulphate reduction. Organic matter is taken to consist of a high‐ and a low‐reactive fraction. The chemical species considered explicitly are PO43−‐P, NO3−‐N, O2, NH4+‐N and H2S‐S. Results indicate that a change from oxic to weakly anoxic conditions at middepths in a P‐limited ocean would lead to strong local denitrification and low nitrate concentrations throughout the water column. New production would also become dominated by nitrogen fixers. Geological evidence implies that anoxic conditions in the water column have been rare in the Phanerozoic ocean. Both phosphorite formation (for P limitation) and denitrification (for N limitation) can strongly constrain primary production and the development of anoxia. N limitation, i.e., negligable nitrogen fixation, practically precludes anoxia but is unlikely for very long times scales. For P limitation and no phosphorite formation the model indicates that the redox state of the ocean may be most sensitive to changes in ocean biology followed by changes in ocean circulation and mixing and finally by changes in ocean temperature.