  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.
