The use of the quaternary semiconductor alloy Ga_xIn_1-xAs_yP_1-y for the development of new electronic, optoelectronic or high speed microwave devices is of great technological interest e.g. in telecommunication. Under certain manufacturing conditions unwanted variations in the chemical composition of these materials can occur, which can be attributed to the existence of a miscibility gap. These decomposition phenomena occur within the nanometer and subnanometer scale. Therefore it is necessary to use characterisation methods of high sensitivity and at the same time highest spatial resolution to investigate independently key parameters such as layer thickness, chemical composition or crystalline structure. The Scanning Transmission Electron Microscope (STEM) is suited for such material analyses since it combines illustrating and analytic characterisation methods together with high spatial resolution. The goal of this work was a comprehensive qualitative and quantitativ e investigation of decomposition in GaxIn1-xAsyP1-y using characterisation techniques like bright-field and Z-contrast imaging as well as electron energy loss spectroscopy (EELS) and convergent beam electron diffraction (CBED), performed in a STEM. For the first time the chemical decomposition process were quantified on the nanometer scale. The course of the decomposition and the predicted expansion of the miscibility gap could be acknowledged in the experiment. Additionally it was shown that by optimising growth parameters (e.g. pressure) of strain compensated superlattices the decomposition process could be inhibited or even stopped. At the same time for the improvement of the evaluation of high resolution Z-contrast images the maximum entropy method (MEM) was applied. Due to the use of the MEM the high resolution Z-contrast images permits the investigation of defect structures and for the first time using a STEM at 100 keV the dumb bells of GaSb was resolved in maximum entropy reconstruction