Conductance-voltage characteristics measured on Ta/Ta2O5/Ag tunneling junctions are strongly asymmetric. A similar result is known for Al/Al2O3/Pb junctions. In the Ta/Ta2O5/Ag case the results are fully consistent with the two-band model for the κ (E) dependence in the oxide barrier. A value of 2 V is obtained for the ’’contact potential’’ describing the barrier asymmetry. This value is well understood on the basis of known electrochemical data for Ta2O5 surface films on Ta. The same mechanism is suggested to apply to Al/Al2O3/Pb junctions.