  A family of the so-called Maxwell times which arises in the contexto of
Higher-Order Generalized Hydrodynamics (also called Mesoscopic
Hydro-Thermodynamics) is evidenced. This is done in the framework of a HOGH
build within a statistical foundation in terms of a Non-Equilibrium Statistical
Ensemble Formalism. It consists in a description in terms of the densities of
particles and energy and their fluxes of all orders, with the motion described
by a set of coupled nonlinear integro-differential equations involving them.
These Maxwell Times have a fundamental role in determining the type of
hydrodynamic motion that the system would display in the given condition and
constraints. The different types of motion are well described by contractions
of the full description done in terms of a reduced number of fluxes up to a
certain order.
