Аннотация:The stability and dynamics of combustion waves in a system consisting of two exothermic solid fuel layers in thermal contact is numerically investigated within the framework of a one-dimensional model. The influence of the thermal interaction between the layers on the stability of combustion waves in the layers is investigated. The characteristics of instabilities and the dynamics of emerging pulsations of the reaction fronts are found to be different for weak and strong thermal coupling. It is shown that with a strong thermal contact between the layers, the stability boundary of a joint system can be significantly expanded.