  Generalized hydrodynamic theory, which does not rest on the requirement of a
local equilibrium, is derived in the long-wave limit of a kinetic equation. The
theory bridges the whole frequency range between the quasistatic
(Navier-Stokes) hydrodynamics and the high frequency (Vlasov) collisionless
limit. In addition to pressure and velocity the theory includes new macroscopic
tensor variables. In a linear approximation these variables describe an
effective shear stress of a liquid and the generalized hydrodynamics recovers
the Maxwellian theory of highly viscous fluids - the media behaving as solids
on a short time scale, but as viscous fluids on long time intervals. It is
shown that the generalized hydrodynamics can be applied to the Landau theory of
Fermi liquid. Illustrative results for collective modes in confined systems are
given, which show that nonequilibrium effects qualitatively change the
collective dynamics in comparison with the predictions of the heuristic Bloch's
hydrodynamics. Earlier improvements of the Bloch theory are critically
reconsidered.
