Production of cumulative particles in nucleon-nucleus interactions is
considered in the framework of the quark-gluon string model. Distribut
ion of quarks in the nucleus is derived under the assumption that cohe
rent clusters exist in the nucleus and their structure functions have
Regge asymptotic behavior. Inclusive spectra of cumulative hadrons (K-
mesons, pi-mesons, pBAR) are analyzed. It is shown that, in this model
, the spectrum of cumulative K--mesons has a behavior similar to that
of K+-mesons, as observed experimentally.