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The formation of image-potential states at the interface between a graphene layer and a metal surface is studied by means of model calculations. An analytical one-dimensional model-potential for the combined system is constructed and used to calculate energies and wave functions of the image-potential states at the $\bar{{\rm{\Gamma }}}$ -point as a function of the graphene–metal distance. It is demonstrated how the double series of image-potential states of freestanding graphene evolves into interfacial states that interact with both surfaces at intermediate distances, and finally into a single series of states resembling those of a clean metal surface covered by a monoatomic spacer layer. The model quantitatively reproduces experimental data available for graphene/Ir(111) and graphene/Ru(0001), systems which strongly differ in interaction strength and therefore adsorption distance. Moreover, it provides a clear physical explanation for the different binding energies and lifetimes of the first ( n = 1) image-potential state in the valley and hill areas of the strongly corrugated moiré superlattice of graphene/Ru(0001).