Using angle-and time-resolved two-photon photoelectron spectroscopy we observe a single series of image-potential states of graphene on monolayer (MLG) and bilayer graphene (BLG) on SiC(0001). The first image-potential state on MLG (BLG) has a binding energy of 0.93 eV (0.84 eV). Lifetimes of the first three image-potential states of MLG are 9, 44 and 110 fs. On hydrogen-intercalated, quasifreestanding graphene no unoccupied states are observed. We attribute this to the absence of occupied initial states for direct transitions into image-potential states at photon energies below the work function used in two-photon photoemission. The work function varies between 4.14 and 4.79 eV, but the vacuum level stays ∼4.5 eV above the Dirac point for all surfaces studied. This finding suggests that direct excitation of image-potential states cannot be achieved by doping and the electron dynamics for free-standing graphene is not accessible by two-photon photoemission using photon energies below the work function.