The anodic reaction on spectrally pure graphite (SPG) and pyrolytic graphite was studied in the potential range from 1.2 to 1.8 V vs. an aluminium reference electrode in alumina-saturated cryolite melts at 1000 degrees C by means of electrochemical impedance spectroscopy. It has been found that the total electrode reaction can be interpreted by a two-step two-electron charge-transfer process with an intermediate adsorption. The experimentally recorded impedance spectra were interpreted in terms of an equivalent circuit approach and the kinetic theory of Bai and Conway, giving the double-layer capacitance, electrode coverage, effective rate constants, and the charge needed for the coverage of the electrode by a monolayer. The process is faster on SPG anode, and on both anodes the second step is faster than the first one.