The aircraft was inbound to Cairns and had requested and was subsequently cleared via a DME (Distance Measuring Equipment) Arrival. When the aircraft was about 45km to the south-east of Cairns the approach controller observed, by radar, that the aircraft had descended below the appropriate level on the arrival procedure. The controller advised the aircraft. However, the crew had realised the error and commenced a climb to the correct level. At the time the aircraft was in visual conditions on top of cloud. The aircraft captain advised that he was instructing another pilot on this flight. The aircraft was slightly off track (although within the tracking tolerances) and the captain had discussed the matter with the Cairns controller and was advising the other pilot on the method of correcting the track error. He did not immediately notice that the aircraft had descended below the appropriate level but corrected the situation when he became aware of the error.