A comparative study, including experiments and molecular dynamic simulation, of the combustion waves in the Ni/Al multilayer reactive nanofoils reveals unknown mechanisms of the process. High speed macro video recording, brightness pyrometry and thermal imaging proved that the combustion wave consists of two stages; the first stage can propagate independently with the same velocity as the complete wave. Products of the first stage of combustion are nano-grains of NiAl separated by liquid gaps of the Al-Ni melt. SEM and TEM study of the intermediate and final products of combustion allow us to suggest a new mechanism of "mosaic" dissolution-precipitation describing nano-heterogeneous reaction at the first stage of the process, which explains dynamics of the combustion wave and resultant microstructure. It was shown also that most of the heat released in the second stage of combustion is generated by grain coarsening. Thus, a conclusion is made that the combustion wave in the Ni/Al reactive multilayer nanofoil is proposed to be a sequential, two stage process involving chemical (first stage) and physical (second stage) exothermic transformations. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.