In the domain of Statistical Mechanics of nonequilibrium-nonlinear (dissipative) systems based on a generalized Gibbs-Boltzmann ensemble formalism,it may be highlighted the so-called Nonequilibrium Statistical Operator Method, and, particularly, Zubarev＇s approach. We report here a detailed analysis of a case consisting in a generalized nonequilibrium grand-canonical ensemble. Its construction requires to introduce besides the traditional densities of energy and the particle number their nonconserving-dissipative fluxes of all order,The description is quite appropriate to provide a framework for the construction of a nonclassical thermo-hydrodynamics, which is briefly described.