Studying of ignition, combustion and detonation processes in dusty gases is presented. The dusty gas is considered as a two-continuum medium with taking into account transport effects in the phases and non-equilibrium chemical reactions. Two-dimensional problems of ignition and detonation developing in a plane gallery caused by a supersonic inflow stream and heating of the closed end of the gallery are studied with the analytical method of catastrophe and two finite-difference numerical methods.