A study is reported of the role played by covalent interaction in the coupling of graphene formed on Ni(111) to the Ni substrate and after intercalation of Au and Cu monolayers underneath the graphene. Covalent interaction of the graphene π states with d states of the underlying metal (Ni, Au, Cu) has been shown to bring about noticeable distortion of the dispersion relations of the graphene electronic π states in the region of crossing with d states, which can be described in terms of avoided crossing effects and formation of bonding and antibonding d–π states. The overall graphene coupling to a substrate is mediated by the energy and occupation of the hybridized states involved. Because graphene formed directly on the Ni(111) surface has only bonding type occupied states, the coupling to the substrate is very strong. Interaction with intercalated Au and Cu layers makes occupation of states of the antibonding and bonding types comparable, which translates into a weak resultant overall coupling of graphene to