Fish need oxygen for aerobic generation of energy for body maintenance, locomotion, feeding and biosynthesis. The rate of oxygen uptake of most fish is limited by diffusion through the gills, and gill surface area grows at a slower rate than body mass. We hypothesize, therefore: (1) that the maximum rate of feed intake is related to the capacity to take in oxygen for processing of this feed; and (2) that the maximum rate of feed intake relative to body size decreases with increasing body size to a point where growth is zero. An oxygen limitation module based on this theory was incorporated into an existing dynamic simulation model for the Nile tilapia, Oreochromis niloticus (L.). The module calculates the maximum potential oxygen supply to the fish on the basis of Fick's law of diffusion and the allometric relationship between body weight and gill surface area. Total oxygen demand of the fish is computed as the sum of routine metabolism, feeding metabolism and energy needed for biosynthesis. In the module, the feeding rate is limited to a level where total oxygen demand does not exceed the potential supply. The model is used to simulate feeding and growth of O. niloticus. Simulation results provide strong support for the oxygen limitation theory. Hence, the model can be used for the analysis of fish growth as affected by feed amount, feed composition, as well as environmental conditions (temperature, dissolved oxygen concentration). It also explains differences in final size between fish species, and within species under different conditions.