The invention relates to a window for use in a supersonic or hypersonic target-tracking missile, the window being transparent to electromagnetic radiation. The window consist of several window layers which support each other and which are commonly supported, wherein the materials, the thickness and the arrangement of said window layers are selected to reduce mechanical stresses due to temperature during supersonic or hypersonic flight as compared to a continuously homogeneous window. In one embodiment the window layers are fixedly interconnected with their surfaces facing each other and consist of materials having different thermal coefficients of dilatation such that, with the temperature gradient occurring in said window during supersonic or hypersonic flight, substantially identical thermal dilatations are achieved in each of said window layers. A further measure is to provide a slip or lubricant layer between the window layers, which slip or lubricant layer allows a relative motion of the window layers parallel to the surfaces facing each other, thereby reducing transmission of stresses between the window layers.