We first study by transmission electron microscopy how the morphological instability of misfitting epitaxial layers depends on the misorientation of the substrate and sign of the misfit. In superlattices containing alternating strained and lattice-matched layers, the surface non-planarity develops by bunching of a large fraction of the original substrates steps for layers under compression, whereas for layers under tension new steps are created. In order to investigate the initial stages of step-bunching and its evolution during growth, we also fabricated homogeneously stressed structures where marker layers were incorporated. Step-bunching is already present after deposition of a few nanometers of material. However, its development does not appear regular during growth. After a first phase where the amplitude of the step bunches increases. we observe its stabilisation and then its decrease. The final part of the paper is dedicated to the study of coupled morphological and compositional instabilities in thick quaternary alloy layers nearly lattice-matched to their substrate. We use X-ray microanalysis to quantify the variations of composition which are coupled with their surface non-planarities.