Both solid- and pore-diffusion models were employed to simulate the adsorption of o-cresol and benzoic acid in a fixed-bed adsorber packed with an anion-exchange resin. The equilibrium adsorption data were modeled by a Langmuir isotherm. When the shape of the adsorption isotherm was approximately linear (as in the case of o-cresol), both models agreed well with the experimental breakthrough data, and they could be effectively applied to predict the breakthrough curve of longer columns. For a favorable adsorption isotherm (say, benzoic acid), however, better results were obtained by using the solid-diffusion model. In addition to the shape of the adsorption isotherm, several factors, such as the type of adsorbent, modeling of equilibrium data, computation efficiency, and concentration dependence of the intraparticle diffusivity, should also be taken into account for selecting a suitable diffusion model.