An examination is made of the possibility of studying diffusion occurring concurrently with another rate process of comparable velocity in penetrant-organic solid systems by means of simple experiments. It is shown that a model of diffusion with time-dependent “thermodynamic” permeability and solubility coefficients offers a useful kinetic description of such systems. Attention is drawn to certain advantages of this approach over earlier similar treatments and to the information which can be obtained by comparing uptake and permeation kinetics. These points are illustrated (with the aid of numerical solutions of the relevant equations where necessary) by detailed discussion of two examples of rate processes which can accompany diffusion, namely: (i) penetrant-induced molecular relaxations in glassy organic solids; and (ii) immobilizing irreversible reaction between the penetrant and suitable groups in the solid. The possibility of quantitative characterization of the accompanying rate process under suitable conditions is also illustrated in example (ii). It is, in fact, shown that considerable information can be obtained about the order and magnitude of the rate constant of the reaction, at least in the simplest systems, by methods similar to those of homogeneous reaction kinetics.