Analysis of the frequency dependence of the impedance of boron-doped diamond thin film electrodes resulted in elucidation of their equivalent circuit. The latter generally comprises a frequency-independent capacitance (or a constant phase element) and a resistance, connected in parallel, with a series-connected "bulk" resistance. For electrodes whose impedance contains a constant phase element, a frequency-dependent Mott-Schottky plot enabled us to determine the flat-band potential. The constant phase element was shown to describe properties of the space charge region in diamond, rather than those of surface states. The behaviour of diamond electrodes is often affected by a series ("Helmholtz") capacitance, which may be compared with the space charge capacitance of a semiconductor.