The results of the studies of a composite based on multiwalled carbon nanotubes (MWCNTs), onto the outer surface of which nanosized copper particles are deposited by the pyrolysis of copper formate, via electron microscopy, X-ray diffractometry, and ultrasoft X-ray spectroscopy, are discussed. It is found that, in an inert argon atmosphere, copper nanoparticles are deposited onto the surface of MWCNTs in the form of different-size nanoparticles consisting of a metallic copper nucleus and a cuprous oxide Cu_2O shell. However, after being taken out into the atmosphere, a layer of copper oxide CuO is formed on the surface of the copper nanoparticles. It is shown that the good adhesion of the copper nanoparticles on the surface of the MWCNTs is provided by the formation of a chemical bond between the carbon atoms of the outer graphene layer of the nanotube and the oxygen atoms of cuprous oxide Cu_2O that initially covers the metallic nucleus of the nanoparticles.