Abstract: For the case of nuclear collisions, the yields of particles with large transverse momenta at mid-rapidities were estimated in the region that is kinematically inaccessible for reactions with single nucleons (the so-called cumulative region). It is assumed that particles in this kinematic region are formed as a result of scattering by the so-called nuclear “fluctons”—clumps of dense quark-gluon matter, including several nucleons and being, from the modern point of view, multiquark clusters. It is shown that in this new cumulative region the yields of pions in comparison with the yields of protons are not suppressed so strongly as in the nuclear fragmentation region, what can be explained by the different mechanisms of the formation of these cumulative particles.