Abstract. The mechanism of current transport in several high k -dielectric, including rare earth metal oxides (Gd 2 O 3 , Nd 2 O 3 ), ternary compounds (LaLuO 3 ) and rare earth metal silicate (LaSiO x ) thin films on silicon was studied using current-voltage ( V I ) and conductance-frequency ( G ) measurements at temperatures 100-300 K. It was shown that the current through the dielectric layer is controlled either by Pool-Frenkel mechanism of trap-assisted tunneling or by Mott's variable range hopping conductance through the localized states near the Fermi level. From the results of measurements, the dynamic dielectric constant k of the material, energy positions and bulk concentrations of traps inside the dielectric layers were determined.