Rayleigh–Taylor instability in a finely structured emulsion-like medium consisting of the two components of different compressibility is considered. Although the term “emulsion” is used to describe the structure of the medium, under typical conditions of pulsed fusion devices the medium is actually a plasma. The two components are chosen in such a way that their densities in the unperturbed state are approximately equal. Specific emphasis has been made on the analysis of perturbations with the scale &slgr; considerably exceeding the size of the grainsa.Average equations describing such perturbations are derived. The difference in compressibility of the two components leads to the formation of temperature variations at the scalea,and increases the rate of the thermal dissipation by a factor(&slgr;/a)2.The strongest stabilizing effect of the thermal dissipation takes place when the heat conduction time is comparable with the instability growth rate. ©1998 American Institute of Physics.