In most cases adsorption onto activated carbon is modelled with no consideration of competing or contaminant species. A recent awareness about this problem of fouling of adsorbents has led to new modelling efforts, such as the formulation of empirical expressions for multi-component isotherms. All these so-called empirical models suffer from the disadvantage that their parameters cannot be used to extrapolate beyond the range of measured data. A brief review of existing methods is provided, so as to indicate the enormous lack of knowledge in this field. The principles of statistical thermodynamics are used to simulate adsorption onto heterogeneous surfaces in terms of a distribution of energies for the active sites, interactions between adsorbed species, the size of adsorbates, the reversibility of adsorption and the selectivity of adsorption. Any adsorption process at equilibrium is described mathematically in terms of the probabilities of collision of a species with the surface, the availability of a site, and the exchange of an adsorbed species with an adsorbing species. In this way the energy distribution and the interaction between species can be determined. These parameters bear a fundamental relevance, and can then be used to predict competitive adsorption for complex systems where available data are inadequate. The competitive adsorption of metal cyanides onto activated carbon is considered as a case study. It is shown that these calculations are complex in view of the numerous statistical calculations involved. However response surface modelling techniques such as neural networks can be used to approximate the surface predicted by the rigorous calculations, which can then be incorporated in the dynamic model simulators. These very powerful theoretical techniques are relatively new in process engineering, but hold much promise for the complex systems encountered in minerals processing.