A Runge-Kutta discontinuous Galerkin method is developed for the model- ing of reactive compressible multiphase flows. From the work developed in [1], where a discontinuous Galerkin formulation was obtained for inert flows based on the ideas of [2] and [3], we introduce a reactive Riemann problem [4] so as to take into account the reactions we are interested in (i.e. reactions with infinitely fast time rates). Several reactive examples are presented. The corresponding results show the high capabilities of the method, which can simulate the strong density and pressure ratios, and also has no problem whenever a phase appears or disappears.