We have investigated the vertical electronic transport in AlN/GaN/AlN double barrier structures grown by plasma‐assisted molecular‐beam epitaxy, with AlN barrier thickness of 0.5 nm and a GaN well thickness varying from 0.5 nm to 2 nm. Two different current levels were observed in different devices in all the samples, the highest one being attributed to leakage through dislocations, and the lower one to tunnelling transport through the barriers. In the sample with a well thickness of 0.5 nm, we observed a bi‐stable behaviour, with an apparent negative differential resistance in the current‐voltage characteristic when scanning the voltage from negative to positive bias. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)