Amorphous alumina films with root-mean-square (r.m.s.) roughnesses of the order of nanometres were deposited on silicon substrates by reactive r.f, sputtering. The surface roughnesses of these films were investigated as a function of the r.f. forward power and the total gas pressure. It was found that the roughness decreased with increasing r.f power. When deposited at low and high gas pressures, the roughness was reduced, whereas it was enhanced at intermediate gas pressures. A rough substrate surface generally resulted in the formation of a rough deposited film. The influence of the film thickness on the surface roughness was not significant. The dependence of the roughness on the r.f. power and gas pressure is interpreted in terms of the atomic shadowing effect and bombardment by negatively charged particles.