A mathematical model of the injection of warm carbon dioxide into a layer of finite length the pores of which are saturated in the initial state with methane and its gas hydrate is constructed. A solution of the problem is presented for the case of the formation of two moving interphase boundaries. In this case, at two different frontal boundaries there occurs the decomposition of the CH4 hydrate into methane, water and the formation of CO2 hydrate from carbon dioxide and liberated water. The dependence of the rate of decomposition of methane gas hydrate on the temperature of the injected carbon dioxide and the initial temperature of the formation is numerically studied, as well as on the pressure values on the right and left boundaries of the formation. It is shown that forming two different boundaries of phase transitions is realized at high temperatures of the formation and injected carbon dioxide. A critical diagram is constructed that determines the "injection temperature-initial reservoir temperature" and "injection pressure-initial pressure of the formation" on the parameter planes in the region of existence of two different process flow regimes. The dependence of the coordinates of both boundaries of phase transitions on time is investigated. It has been established that over time the formation boundaries of CO2 hydrate and the decomposition boundaries of the CH4 hydrate can be merged. The influence of heat released during the formation of the CO2 hydrate on the acceleration of the decomposition of the CH4 hydrate was studied. It was found that the latent heat of formation of the CO2 hydrate markedly increases the rate of decomposition of CH4 hydrate, and the contribution of this heat to the rate of decomposition of the hydrate increases with decreasing temperature of the injected gas. (C) 2018 Elsevier Ltd. All rights reserved.