15-15U

Within the frame of a standard scheme of the non-equilibrium statistical theory the perturbation theory for time correlation function (TCF) in matrix form is developed. In general from the series of perturbation theory for the kinetic matrix are found, and the correlations to collective modes to TCFs are calculated. The case of small off-diagonal cross-correlations is studies in details and TCF for this case are received. It is shown that the sum rules of null order for off-diagonal TCFs are satisfied in the first order of the perturbation theory developed.