The decay to equilibrium is discussed from a general point of view based on the assumed rapid approach to local equilibrium for well-chosen initial states. The assumption is applied to the problem of time correlation functions and it is shown that the mode-coupling formula describes the asymptotics of the so-called projected wavenumber-dependent correlation functions. The local equilibrium assumption thus provides a general basis for thet –3/2 behavior of correlation functions derived in previous papers in this series, as well as for the infinite series of correction termst –(2–Pn (n 2), withPn=2–n, and for the corresponding series of corrections of orderk 3–Pn (n1) to Navier-Stokes hydrodynamics.