  We study tight-binding models of itinerant electrons in two different bands,
with effective on-site interactions expressing Coulomb repulsion and Hund's
rule. We prove that, for sufficiently large on-site exchange anisotropy, all
ground states show metallic ferromagnetism: They exhibit a macroscopic
magnetization, a macroscopic fraction of the electrons is spatially
delocalized, and there is no energy gap for kinetic excitations.
