Gas diffusion in coals plays an important role in enhanced coalbed methane production, fugitive gas emissions from coal, and gas release in coal mines. However, a consistent picture of diffusion behaviour in coals is yet to emerge. For example, the adequacy of describing diffusion by a single coefficient is debated. Moreover, some researchers have reported diffusion coefficients as increasing with rising pressure, others report the opposite. This variation may be due to the choice of the model, coal, or experimental conditions. In this study, experimental CO2 kinetic sorption data was obtained for two Australian bituminous coals over a range of pressure conditions and analysed using three different models. We found that the unipore model, which uses only one characteristic diffusion coefficient, does not adequately capture the sorption kinetics. Using a bidisperse model, two characteristic coefficients can describe the diffusion process. The pressure dependence of the fast diffusion coefficient decreases as the system pressure rises. However, the slow diffusion coefficient is not solely dependent on pressure, but is influenced by additional sorption by the coal, which is introduced during the pressure step. Depending on the amount of gas sorbed in a single sorption step, the magnitude of the slow diffusion component will change. This diffusion coefficient exhibits concentration dependence; it varies depending on whether small or large pressure steps are applied. This suggests that the bidisperse model used is inappropriate for examining the pressure dependence of diffusion coefficients at these conditions. Experiments were repeated using a microporous activated carbon, where CO2 uptake displayed rapid kinetics, with no evidence of a slower component This indicates that the slower uptake of CO2 observed in coal is due to specific properties of the coals. A Fickian diffusion-relaxation model (FDR) developed for studying anomalous diffusion in glassy polymers is proposed instead, ascribing the diffusion in the primary stage to Fickian diffusion, and in the second stage due to slow rearrangement of the coal structure possibly associated with swelling. Additionally, the rapid uptake of gas by the coals (investigated by the model fits) is found to be very sensitive to measured sorption values immediately after gas exposure. This affects the magnitude of calculated diffusion coefficients. (C) 2013 Elsevier B.V. All rights reserved.