  In the framework of the non-local dielectric theory the static non-local
self-energy of an electron near an ultra-thin polarizable layer has been
calculated and applied to study image-states near free-standing graphene. The
corresponding series of eigenvalues and eigenfunctions have been obtained by
solving numerically the one-dimensional Schr{\"o}dinger equation. We compare
with the Rydgberg's series for a perfect metal and with experimental values
measured on graphene layers grown on Ir and Ru surfaces. For free standing
films, the appearance of states with binding energies in between the classical
series is discussed.
