Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities are considered in a fluid layer of thicknessthaving perturbations of arbitrary wave numberkat either one or both interfaces. The evolution of the perturbation amplitudes &eegr;1,2(&tgr;), &tgr; =time, is given analytically in terms of a coupling angle &thgr; which measures the strength of the coupling between interfaces 1 and 2. A new type of freeze‐out in shocked layers is reported according to which, the proximity of the two interfaces can, under proper conditions, lead to the complete freeze‐out of one, but not both, perturbations. For example, to freeze the first interface one needs &eegr;1(0)/&eegr;2(0)= sin &thgr;. Freeze‐out cannot be achieved in the RT case; instead, one can kill one of the modes. For example, setting &eegr;1(0)/&eegr;2(0)= tan(&thgr;/2) will kill the exponentially growing mode, leaving only the oscillatory mode at both interfaces. ©1995 American Institute of Physics.