High-resolution electron energy-loss spectroscopy (HREELS), low-energy electron diffraction, and X-ray photoelectron spectroscopy have been used to study clean 825 K-preannealed alpha-Fe2O3-1X1 (haematite) surfaces, an alpha-Fe2O3-(0001)-1x1 surface reconstructed with Fe3O4(111)-1x1 and to study Cu deposited on room temperature surfaces of those. Three pronounced losses, at 47.5, 55.5 and 78.0 meV, of the surface phonons for the clean alpha-Fe2O3(0001) were observed. By deposition of copper, Cu-O vibrational features observed by HREELS indicate formation of a Cu(I) state for the very low coverages. Increased submonolayer amounts of Cu result in clustering of the copper, leading for both the alpha-Fe2O3(0001)-1 x1 and the reconstructed composite substrate surfaces to Cu(111) epitaxial growth.