The review considers thermodynamics and kinetics of isotope exchange in the H2O-H2S system. The temperature dependences of separation factor a are considered for all binary H-T, H-D, and DT mixtures. The effect of equilibrium constants of homo-molecular exchange reactions involving water and hydrogen sulfide on concentration dependence of a is demonstrated. Distribution of tritium between the liquid and the gas phases has been studied as a function of the HID ratio in each phase. The differential equations describing the steady-state interdiffusion of dissolved hydrogen sulfide and water accompanied by chemical reaction of isotope exchange have been solved. It has been shown that solution to the mass-transfer problem allows for calculation of the HTU (height of transfer unit) value in a packed separation column. The HTU dependences on the flowrate in a packed column and on the composition of liquid-phase in the H2O-H2S and D2O-D2S systems are presented. A mathematical model of isotope separation by the dual-temperature method is discussed. The model is used to analyze the basic features of the method and the effects associated with mutual solubility of phases. Optimization of the Girdler-Spevack process by varying the operation parameters in the column are discussed. The results of testing a modified dual-temperature set-up demonstrate a high efficiency of separation of hydrogen isotopes by the proposed technique.