In the framework of the modified FRITIOF model, the inclusive spectra of the cumulative $pi ^0$-, $pi ^- $-mesons and protons produced in the nucleus-nucleus interactions at 4.5 GeV/c/nucleon and 4.2 GeV/c/nucleon are calculated. It is shown that the model reproduces qualitatively, and in some cases quantitatively the main experimental regularities of $pi$-mesons production, and soft part of the proton spectra. According to the model the production of the cumulative particles is connected with the mechanism of the soft nucleon-nucleon interaction.
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