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Observations have shown that large areas of the world ocean are characterized by lower than expected chlorophyll concentrations given the ambient phosphate and nitrate levels. In these High Nutrient‐Low Chlorophyll regions, limitations of phytoplankton growth by other nutrients like silicate or iron have been hypothesized and further evidenced by in situ experiments. To explore these limitations, a nine‐component ecosystem model has been embedded in the Hamburg model of the oceanic carbon cycle (HAMOCC5). This model includes phosphate, silicate, dissolved iron, two phytoplankton size fractions (nanophytoplankton and diatoms), two zooplankton size fractions (microzooplankton and mesozooplankton), one detritus and semilabile dissolved organic matter. The model is able to reproduce the main characteristics of two of the three main HNLC areas, i.e., the Southern Ocean and the equatorial Pacific. In the subarctic Pacific, silicate and phosphate surface concentrations are largely underestimated because of deficiencies in ocean dynamics. The low chlorophyll concentrations in HNLC areas are explained by the traditional hypothesis of a simultaneous iron‐grazing limitation: Diatoms are limited by iron whereas nanophytoplankton is controlled by very efficient grazing by microzooplankton. Phytoplankton assimilates 18 × 10 9 mol Fe yr −1 of which 73% is supplied by regeneration within the euphotic zone. The model predicts that the ocean carries with it about 75% of the phytoplankton demand for new iron, assuming a 1% solubility for atmospheric iron. Finally, it is shown that a higher supply of iron to surface water leads to a higher export production but paradoxically to a lower primary productivity.