Using molecular beam mass spectrometry of high temporal and spatial resolution, periodical changes in the partial pressures of boron and carbon oxides and suboxides were found whilst combustion waves propagated in the systems: Mo + B, Nb + 2B, and Ta + C. These pressure pulsations are attributed to auto-oscillations of the combustion wave in the systems under study. Kinetic and thermodynamic analyses show that these pulsations, as well as the 1-D instability in solid-state combustion, are caused by a combination of fast heterogeneous reactions of suboxides in the reaction zone, controlled by their relatively slow formation in the heat-affected zone. The reaction structure of the combustion wave and an appropriate kinetic model of the process are suggested. (C) 2000 by The Combustion Institute.