The growth of oxide films on aluminium nitride substrates covered by vapour-deposited aluminium films of 1.5 and 4 mum thickness has been studied in air at atmospheric pressure as a function of temperature. Oxide films were grown by oxidation in air at temperatures between 800 and 1300-degrees-C. The kinetics of the growth of oxide films on such substrates was observed to be complex. In particular, there are three subsequent periods of observed oxide growth : (1) an initial period of rapid oxide growth, (2) an incubation period with very slow oxide growth, and (3) a second period of relatively fast oxide growth.