Materials of mesoscopic dimensions can be produced by modern scanning microscopic and chemical techniques. This opens the possibility of creating new nanoscale magnets, which consist only of a few atoms. These systems may exhibit novel and unusual properties. We demonstrate, that metamagnetic states are possible in supported metallic nanostructures. This effect can lead to magnetic transitions between different magnetic states by a change of external parameters like temperature or applied fields. We apply the local approximation of the density functional theory and a recently developed KKR Green's function method to supported clusters. A detailed consideration of the Cu(001) surface with 3d supported metallic nanostructures is presented.