  By using a time-dependent operator converting a distribution function
(statistical operator) of a total system under consideration into the relevant
form, new exact nonlinear generalized master equations (GMEs) are derived. The
inhomogeneous nonlinear GME is a generalization of the linear Nakajima-Zwanzig
GME and is suitable for obtaining both the linear and nonlinear evolution
equations. To include initial correlations into consideration, this
inhomogeneous nonlinear GME has been converted into the homogenous form by the
method suggested earlier in [9], [10]. Obtained homogeneous nonlinear GME
describes all stages of the (sub)system of interest evolution and influence of
initial correlations at all stages thereof. In contrast to homogeneous linear
GMEs obtained in [9], [10], the homogeneous nonlinear GME is convenient for
getting both a linear and nonlinear evolution equations. The obtained nonlinear
GMEs have been tested on the space inhomogeneous dilute gas of classical
particles. Particularly, a new homogeneous nonlinear equation describing an
evolution of a one-particle distribution function at all times and retaining
initial correlations has been obtained in the linear in the gas density
approximation. This equation is closed in the sense that all two-particle
correlations (collisions), including initial ones, which contribute to
dissipative and nondissipative characteristics of the nonideal gas are
accounted for. Connection of this equation at the kinetic stage of the
evolution to the Vlasov-Landau and Boltzmann equations is discussed.
