  In the framework of the recently proposed QCD based parton model for the
cumulative phenomena in the interactions with nuclei two mechanisms for
particle production, direct and spectator ones, are analysed. It is shown that
due to final state interactions the leading terms of the direct mechanism
contribution are cancelled and the spectator mechanism is the dominant one. It
leads to a smaller slope of the cumulative particle production rates compared
to the slope of the nuclear structure function in the cumulative region $x>1$,
in agreement with the recent experimental data.
