The results of a transmission electron microscopy study of Co/Au and Co/Pd multilayers are reported. Special emphasis is put on the epitaxial growth and the relaxation of the misfit strain of these high misfit systems. In bright-field cross-sectional images, periodic contrast fringes are observed at the interfaces, which are the result of Moiré interference and which allow determination of the degree of misfit relaxation at the interface. It was established that 80-85% of the misfit is relaxed. From high resolution electron microscopy images the Burgers vector of the misfit dislocations was derived, being a/2<110> lying in the (111) interface plane. The results obtained for the Co/Au and Co/Pd multilayers will be discussed in comparison with those obtained for a bilayer of Co and Au.