Traditional transport models have failed to account for uptake of many protein-bound ligands by liver and other tissues when the concentration of plasma albumin or other binding protein is varied. In this paper, we extend the standard sinusoidal perfusion model to include the effects of slow dissociation of the ligand from albumin and of diffusion across extracellular barriers such as the unstirred layer. We then use experimental data for uptake of oleate from albumin solutions (1:10 molar ratio) by perfused female rat livers to test this model. Unlike the standard model, the extended model closely conformed to observed uptake rates over a wide concentration range (0.015-0.45 mM albumin). The extension, which is conceptually simple, is based on widely accepted physiological principles. It requires only the introduction of two dimensionless ratios into the standard model: the ratio of the mean unbound ligand concentration actually present within the capillary or sinusoid to its equilibrium value, and the ratio of the permeability of the membrane plus associated extracellular diffusion barriers to the permeability of the membrane alone. The resulting model simplifies to the standard sinusoidal perfusion model when both ratios approximate unity. We first develop the model for steady influx alone because our data suggest that little efflux of oleate occurred over the time course of the current study. In an appendix, we extend the model to include the effects of efflux and metabolism. The new model offers an alternative for explaining uptake kinetics of protein-bound ligands that cannot be explained by less complete traditional models.