  In the paper we discuss possible approaches to the problem of the rigorous
derivation of quantum kinetic equations from underlying many-particle dynamics.
For the description of a many-particle evolution we construct solutions of the
Cauchy problems of the BBGKY hierarchy and the dual BBGKY hierarchy in suitable
Banach spaces. In the framework of the conventional approach to the description
of kinetic evolution the mean-field asymptotics of the quantum BBGKY hierarchy
solution is constructed. We develop also alternative approaches. One method is
based on the construction of the solution asymptotics of the initial-value
problem of the quantum dual BBGKY hierarchy. One more approach is based on the
generalized quantum kinetic equation that is a consequence of the equivalence
of the Cauchy problems of such evolution equation and the BBGKY hierarchy with
initial data determined by the one-particle density operator.
