Annihilation cross-sections sigma(ann) for antineutrons on some nuclei (C, Al, Cu, Sn and Pb) at three antineutron momenta (180, 240 and 280 MeV/c) were measured at LEAR (CERN) with the OBELIX spectrometer. A behaviour sigma(ann) = = sigma0A(nu) has been found with nu almost-equal-to 2/3. The data are discussed following some models for antineutron-nucleus interaction.