  We develop a rigorous formalism for the description of the evolution of
observables of quantum systems of particles in the mean-field scaling limit.
The corresponding asymptotics of a solution of the initial-value problem of the
dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution
of marginal observables and the evolution of quantum states described in terms
of a one-particle marginal density operator are established. Such approach
gives the alternative description of the kinetic evolution of quantum
many-particle systems to generally accepted approach on basis of kinetic
equations.
