Halide nucleation and growth on monocrystalline copper substrates under molecular halogens action was studied by means of Auger Electron Spectroscopy (AES) and Scanning Tunnelling Microscopy (STM). It was found that copper iodide grows on Cu(100) and Cu(111) in a layer-by-layer mode with its outer hexagonal plane parallel to the substrate surface. The STM images of copper iodide demonstrate Moiré-like superstructures. The nature of these superstructures is explained in terms of superposition of the copper iodide layer and the underlying interface monolayer. It was found that the interface layer preserves geometrical and electronic structure of the saturated chemisorbed iodine monolayer for both copper planes. Moreover, we have found out that orientation of copper iodide nuclei on a surface strongly depends on the step edges orientation, which, in turn, is determined by the direction of close-packed atomic rows in the saturated iodine monolayer. [DOI: 10.1380/ejssnt.2004.234]