X-ray photoelectron spectroscopy (XPS) is used to study the electronic states of copper oxide covering a thin (2.0 +/- 0.5 nm) layer of ultradisperse copper. A reduction in the thickness of the CuO layer is found to cause extremal behavior in the XPS spectrum parameters as opposed to their monontonic variations for CuO nanoparticles. This behavior is explained by the competition of two factors which affect the system under study: the dimensions of the substrate material and the electrostatic field in it.