A three-phase (gas-liquid-adsorbent) mass-transfer operation, called exsorption, which may have potential in chemical, biochemical and environmental processes, is described. The system of interest consists of a column packed with adsorbent particles through which gas and liquid streams flow in countercurrent mode. Distributed-parameter models, which assume isothermal operation and transfer of a single solute among the mutually immiscible phases, are presented for the two different wetting states of adsorbent particles. Equilibrium theory of exsorption is established on the basis of the distributed-parameter models of the system. The equilibrium theory predicts various aspects of propagation dynamics of concentration waves and reveals individual-relative effects of concentration dependence of gas-liquid, liquid-adsorbent and gas-adsorbent equilibrium isotherms. Based on the characteristics of the equilibrium isotherms, criteria for the development of sharpening, spreading, and stagnant concentration waves can be obtained directly from the equilibrium propagation velocity of the system. The equilibrium theory of exsorption is compared with the equilibrium theories of fixed-bed adsorption and countercurrent gas-liquid mass-transfer operations.