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We apply a linear stability analysis to examine the effect of misfit stress on the interface diffusion controlled morphological stability of multilayer microstructures. The stresses could be the result of misfit strains between the individual film layers and/or between film and substrate. We find that misfit between the layers in the film can destabilize the multilayer structure in cases where the thinner layer is elastically stiffer than the thicker layer. The rate at which these instabilities develop increase with increasing misfit and decreasing interfacial energy. Even when there is no misfit between layers, the misfit between the multilayer film and substrate can destabilize the interfaces. This type of instability occurs whether the thinner layers are stiffer or more compliant than the thicker ones. By appropriate choice of the elastic moduli mismatch between layers and relative layer thicknesses, the presence of an interlayer misfit can suppress the instability caused by the substrate misfit. We present stability diagrams that can be used to design stable, multilayer films using all of the degrees of freedom commonly available in multilayer film deposition. © 1997 American Institute of Physics.