Resonant tunnelling diodes of cubic Al(Ga)N/GaN were grown by plasma assisted molecular beam epitaxy on 3C-SiC (001). We observe a pronounced negative differential resistance at about 1.2 V with a peak-to-valley ratio (PVR) of 1.3 to 2.7 at room temperature. Experimental data is in good agreement with calculated I–V curves showing only a small deviation of 0.3 V of the resonance peak voltage. We find a decrease of the PVR when the I–V characteristic is measured repeatedly with short time intervals between the voltage-cycles. However, the I–V characteristics can be recovered fully when the diodes are illuminated by UV-light indicating charge trapping in our devices. Mesa structures are prepared by reactive ion etching. The size of the top ohmic contacts is (25 × 11) µm2. The Al content of the barrier material is varied between 30% and 100%.