In this letter we present results on the growth of InAs nanowires (NW's) on InGaAs lattice-matched to (100) InP substrates by Chemical Beam Epitaxy. We observed that the nanostructure stability depends on the thickness of the InGaAs layer. This effect may result from two different conditions: the nanostructure strain field depth and/or compositional modulation in the buffer layer. Our investigation shows that anisotropic strain relaxation for nanowires grown on InGaAs is faster than for those grown on InP but the elastic energy in the nanostructures is no different from the InAs/InP case. These results suggest that the InAs strain relaxation does not depend significantly on the InGaAs buffer layer thickness. Nevertheless, transmission electron microscopy images show an additional stress field superimposed on that usually observed for the InAs nanostructures, which is attributed to compositional modulation in the ternary layer.