Interest in the mode of propagation of self-sustaining reactions has been motivated by the influence of the mode on the microstructure and composition of the final product. However, comprehensive studies relating the onset of the various propagation modes to the chemical and phase transformations taking place in the sample are still lacking. In the present work propagation instabilities in self-propagating high-temperature synthesis (SHS) of transition metal aluminides are studied using a computer simulation approach. The results are presented for the SHS of NiAl, CoAl, TiAl, and NbAl3. Particular emphasis is made with respect to the influence of process variables and system parameters on the onset of propagation instabilities, in relation to the physicochemical processes taking place during the propagation of the combustion front.