  In the paper we consider the problem of the rigorous description of the
kinetic evolution in the presence of initial correlations of quantum large
particle systems. One of the developed approaches consists in the description
of the evolution of quantum many-particle systems within the framework of
marginal observables in mean field scaling limit. Another method based on the
possibility to describe the evolution of states within the framework of a
one-particle marginal density operator governed by the generalized quantum
kinetic equation in case of initial states specified by a one-particle marginal
density operator and correlation operators.
