  A chain of kinetic equations for non-equilibrium one-particle, two-particle
and $ s $-particle distribution functions of particles which take into account
nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev
non-equilibrium statistical operator with projection is used. Nonlinear
hydrodynamic fluctuations are described with non-equilibrium distribution
function of collective variables that satisfies generalized Fokker-Planck
equation. On the basis of the method of collective variables, a scheme of
calculation of non-equilibrium structural distribution function of collective
variables and their hydrodynamic speeds (above Gaussian approximation)
contained in the generalized Fokker-Planck equation for the non-equilibrium
distribution function of collective variables is proposed. Contributions of
short- and long-range interactions between particles are separated, so that the
short-range interactions (for example, the model of hard spheres) are described
in the coordinate space, while the long-range interactions --- in the space of
collective variables. Short-ranged component is regarded as basic, and
corresponds to the BBGKY chain of equations for the model of hard spheres.
