The marine diatom Thalassiosira weissflogii (Grunow) G. A. Fryxell & Hasle was grown in a chemostat over a series of phosphate-limited growth rates. Ambient substrate concentrations were determined from bioassays involving picomolar spikes of 33P-labeled phosphate, and maximum uptake rates were determined from analogous bioassays that included the addition of micromolar concentrations of unlabeled phosphate and tracer concentrations of 33P. The relationship between cell phosphorus quotas and growth rates was well described by the Droop equation. Maximum uptake rates of phosphate spikes were several orders of magnitude higher than steady state uptake rates. Despite the large size of the T. weissflogii cells, diffusion of phosphate through the boundary layer around the cells had little effect on growth kinetics, in part because the cellular N:P ratios exceeded the Redfield ratio at all growth rates. Fitting the Monod equation to the experimental data produced an estimate of the nutrient-saturated growth rate that was ~50% greater than the maximum growth rate observed in batch culture. A modified hyperbolic equation with a curvature that is a maximum in magnitude at positive growth rates gave a better fit to the data and an estimate of the maximum growth rate that was consistent with observations. The failure of the Monod equation to describe the data may reflect a transition from substrate to co-substrate limitation and/or the presence of an inducible uptake system.