Current models of self-propagating reactions in multilayer foils have been successful in predicting the velocity and structure of reaction fronts, as well as their variation with individual layer thickness and premixing in the as-deposited state. Depending upon the parameter regime, the propagation of the reaction front has been shown to occur either in a steady manner or in an oscillatory manner. So far, however, existing models have ignored the effect of heat lasses on the reaction. In this study, the effect of radiative and conductive heat losses on the propagation of reaction fronts in multilayers is investigated numerically. Heat losses are shown to decrease the flame speed and the magnitude of the oscillations, and to increase the period of the oscillations. In the parameter range considered, radiative heat losses have a much smaller effect on reaction propagation than conductive heat losses. (C) 2001 by The Combustion Institute.