Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)A kinetic equation for the single particle distribution function in an open many-body system, when in far away from equilibrium conditions is derived in the context of a Non-Equilibrium Thermo-Statistics of ample scope. It consists of a generalization of traditional kinetic equations in that no restrictions are imposed on the characteristics of the nonequilibrium thermodynamic state of the system. This kinetic equation do contain some contributions that become relevant in systems with a nonlinear kinetics when driven sufficiently far from equilibrium (certain complex systems). Moreover, the handling of the kinetic equation in a multiple-moment approach provides a generalized nonlinear higher-order thermo-hydrodynamics.143510201034Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)