Four films (A, B, C and D) of discontinuous platinum films (D(Pt)Fs) whose mass thicknesses (d m ) are 10, 20, 30 and 40 Å , respectively were deposited onto Corning 7,059 glass substrates at ambient temperature via the thermal evaporation technique. Each film was c-irradiated by different doses, namely, 100, 200, 300, 500 and 700 Gy; this was done by using 137 Cs (0.662 MeV) radiation source of dose rate 0.5 Gy/min. For each dose, the d. c. and total resistance of the Pt films were measured; in that way the a.c. conductance G ac of the films could be determined. It was found that: (1) G ac increases as the dose, d m and the angular frequency x of the voltage imposed on the film increases (2) the c-irradiation has modified the shape of islands such that they are elongated parallel to the substrate surface and thus the inter-island spacings have decreased. This elongation has been confirmed via micrographs taken by the atomic force microscope. To account qualitatively for the results of G ac it was assumed that, the a.c. conductance of D(Pt)Fs is due to the hopping of electrons through the sites which exist on the substrate surface between two adjacent islands.