[en] The intranuclear-cascade model is developed for inelastic interactions between antinucleons (also antideuterons) and nuclei at energies up to 10 GeV. The model includes the effects of the local reduction of the nuclear density during the development of the cascade and the production of mesonic resonances and their subsequent interaction with the nuclear medium, and takes into account the deexcitation of the residual nuclei through evaporation and multifragmentation. These improvements enable the authors to compare the calculations with experiment. New physical phenomena which become noticeable in the antinucleon-nucleus interaction are discussed. 36 refs., 14 figs