The adsorption kinetics of many systems show apparent two-rate processes, where there appears to be resolved fast and slow adsorption steps. Such non-standard adsorption processes cannot be accounted for by conventional modeling methods, motivating new approaches. In this work, we present four different models that can account for two-rate adsorption and are based upon physically realistic processes- two adsorbing species, two surface sites having different energies, bilayer formation and molecular rearrangement modes. Each model is tested using a range of conditions, and the characteristic behavior is explored and compared. In these models, the effects of mass transport and bulk concentration are also accounted for, making them applicable in systems which are transport-limited or attachment-limited, or intermediate between the two. The applicability of these models is demonstrated by fitting exemplar experimental data for each of the four models, selecting the model on the basis of the known physical behavior of the adsorption kinetics. These models can be applied in a wide range of systems, from stagnant adsorption in large volume water treatment to highly dynamic flow conditions relevant to printing, coating and processing applications. (C) 2016 Elsevier Inc. All rights reserved.