We develop two mathematical models for coupled solute transport and nonlinear adsorption to geologic media. Both models quantify nonuniformity in mass transfer rates with parameters that vary according to a gamma (&ggr;) probability density function. The multisite model, which describes surface-reaction controls on adsorption kinetics, solves equations for a second-order rate law. The adsorption rate coefficient of the kinetics equation is correlated with a &ggr;-distributed desorption rate coefficient. The mobile-immobile model is based on the assumption that rate limitations are diffusion controlled and account for a &ggr; distribution in solute exchange rates between zones of mobile and immobile water. Solute adsorption in the immobile zone is quantified with the nonlinear expression for the Langmuir equilibrium isotherm. We test the models against results of column experiments on the transport of hydroxyatrazine (HA), a persistent contaminant produced from the degradation of atrazine. We find that the experimental data are matched more closely by calculations of the multisite model than by calculations of the mobile-immobile model, suggesting that HA adsorption can be understood best as a kinetics reaction with a solid phase composed of binding sites with a broad distribution in adsorption and desorption energies. ¿ 2000 American Geophysical Union