The specific capacitanceCsof Nb/AlOx/Nb Josephson tunnel junction has been measured by means of the superconducting quantum interference device (SQUID) resonance technique. We have investigated the junctions with critical current densitiesJcin the range of 0.1–18 kA/cm2and found that 1/Cslinearly depends on a logarithm ofJc. This suggests that the barrier thickness is moderately uniform in the junction area and increases continuously during growth. The results also show that increasingJcreduces time constants of the junction. ©1995 American Institute of Physics.