  This paper is devoted to the problem of the description of nonequilibrium
correlations in quantum many-particle systems. The nonlinear quantum BBGKY
hierarchy for marginal correlation operators is rigorously derived from the von
Neumann hierarchy for correlation operators that give an alternative approach
to the description of states in comparison with the density operators. A
nonperturbative solution of the Cauchy problem of the nonlinear quantum BBGKY
hierarchy for marginal correlation operators is constructed.
