Molecular beam epitaxy has been used to prepare multiple quantum well structures of CdTe/Cd1−xMnxTe on (001) InSb substrates. The growth of such a system on InSb allows the use of particularly low growth temperatures, hence minimizing interdiffusion effects. This study presents the first transmission electron microscope investigation of this multilayer system grown on InSb. The work clearly demonstrates that multiple quantum wells of high structural quality can be grown reproducibly over a wide range of layer thicknesses. The importance of efficient substrate surface cleaning prior to growth is demonstrated. In order to grow high structural quality multilayers, the choice of buffer layer is also important and a possible explanation for this observation is given.