Multilayered face-centered cubic Co/Pt and CoNi/Pt nanostructures grown on a Pt(111) or Cu(111) single-crystal substrate by electrodeposition under potential control, respectively, exhibit a remanent perpendicular magnetization and a large magnetic coercivity, which depend on the multilayer growth mechanism. The role of the codeposition of Ni as an inhibitor for the nucleus growth process as well as for the dissolution of Co during the Pt deposition is of great importance for the occurrence of the multilayered nanostructure.