The I(V) and I(T) characteristics of diamond films after various treatments are reported and analysed. The ohmic behaviour of contacts on as-grown films originates from a superficial conductive layer making an ohmic contact with diamond. Annealing of the films at 600-degrees-C under argon or vacuum keeps this ohmic behaviour. In contrast, annealing under oxygen, or nitrogen, or air, induces a non-linear, very high contact resistance. In this case the electrical properties are ascribed to a metal-insulator-semiconducting-diamond structure, with a depletion layer and a potential barrier height of 0.85 eV between the diamond band and the Fermi level at the diamond-insulator interface. The superficial insulating layer results from oxidation of the as-grown porous superficial conductive layer, which is in agreement with the oxygen-carbon reactions reported for these experimental conditions.