A complete theory for investigation of time correlation functions is developed on the basis of the Bogolyubovudreduced description method proceeding from his functional hypothesis. The problem of convergence in theudtheory of nonequilibrium processes and its relation to the non-analytic dependence of basic values of theudtheory on a small parameter of the perturbation theory are discussed. A natural regularization of integraludequations of the theory is proposed. In the framework of a model of slow variables (hydrodynamics of a fluid,udkinetics of a gas) a generalized perturbation theory without divergencies is constructed corresponding to audpartial summation in a usual perturbation theory. Properties of Green functions are discussed on the basis ofudresolvent formalism for the Liouville operator. A generalized Ernst and Dorfman theory is elaborated allowingudto study the peculiarities of correlation and Green functions and to solve the convergence problem in theudreduced description method.
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