MoO₂ nanotube with rectangular cross sections can be prepared on Mo substrates by using an O₂-C₂H₂ combustion-flame method [Jpn. J. Appl. Phys. 44 (2005) L449]. We have investigated the growth behavior of the nanotube in detail by using scanning electron microscopy and energy dispersive x-ray microanalysis. The precursor of the growth is produced onsite at the Mo substrate, through reactions with oxygen radicals supplied from the combustion flame. The precursor is then transferred, in the flow of the combustion flame, to the backside of the substrate to form the rectangular nanotube. The growth is accompanied by oxidation, which is crucial in determining the shape of the nanostructure. A two-stage growth model, consisting of initial bulk-cluster growth and subsequent growth of nanotube, is proposed based on the observations. [DOI: 10.1380/ejssnt.2009.307]