  Construction, in the framework of a Nonequilibrium Statistical Ensemble
Formalism, of a Mesoscopic Hydro-Thermodynamics, that is, covering phenomena
involving motion displaying variations short in space and fast in time
-unrestricted values of Knudsen numbers-, is presented. In that way, it is
provided an approach enabling for the coupling and simultaneous treatment of
the kinetics and hydrodynamic levels of descriptions. It is based on a complete
thermo-statistical approach in terms of the densities of matter and energy and
their fluxes of all orders covering systems arbitrarily driven away from
equilibrium. The set of coupled nonlinear integro-differential hydrodynamic
equations is derived. They are the evolution equations of the Grad-like moments
of all orders, derived from a kinetic equation built in the framework of the
Nonequilibrium Statistical Ensemble Formalism. For illustration, the case of a
system of particles embedded in a fluid acting as a thermal bath is fully
described. The resulting enormous set of coupled evolution equations is of
unmanageable proportions, thus requiring in practice to introduce an
appropriate description using the smallest possible number of variables. We
have obtained a hierarchy of Maxwell-times, which can be considered a kind of
Bogoliubov's characteristic times in hydrodynamics and which have a particular
relevance in the creteria for stablishing a contraction of description.
